Physics Chapter 8 - ALL IN ONE
Inertia depends on mass; rotational inertia depends on mass and something else. What?
The distribution of mass about the axis of rotation
Which is easier to get swinging: a baseball bat held at the narrow end or a bat held closer to the massive end (choked up)? Also answer for a short bat versus a long bat.
The easiest is choked up and a short bat.
Calculate the tension in a horizontal string that whirls a 2.4-kg toy in a circle of radius 2.4 m when it moves at 3.2 m/s on an icy surface.
10N
the filled jar
Neglecting air resistance, which will roll from rest to the bottom of an incline first, an empty jar, or the same jar filled with peanut butter?
The average position of weight or the single point associated with an object where the force of gravity can be considered to act.
Center of gravity (CG)
The average position of the mass of an object. The CM moves as if all the external forces acted at this point.
Center of mass (CM)
Where is the center of mass of a hollow soccer ball?
In the center of the ball
Distinguish between tangential speed and rotational speed.
Tangential speed(velocity) in m/s forward motion. Rotational speed in R.P.M. is the turning motion
Describe the comparative stablities of the three objects shown in terms of word and potentional energy.
The 1st is the least change in PE and the 3rd recuires the most work....
Which will have the greater acceleration rolling down an incline: a bowling ball or a volleyball? Defend your answer.
A bowling ball, because a solid sphere has less rotational inertia per mass than other shapes. Its mass is near the rotational axis that extends through its center of mass.
is the disk
A ring and a disk, initially at rest, roll down a hill together. The one to reach the bottom first
What is the relationship between the center of gravity and the support base for an object that is in stable equilibrium?
A vertical line through the center of gravity must pass inside the support base of the object.
Why can't you stand with your heels and back to a wall and then bend over to touch your toes and return to your stand-up position?
A vertical line through the center of gravity of your body is in front of the tips of your toes, which is outside your support base.
Why doesn't the Leaning Tower of Pisa topple over?
A vertical line through the center of gravity passes inside its support base.
An outward force apparent in a rotating frame of reference. It is apparent (fictitious) in the sense that it is not part of an interaction but is a result of rotation--with no reaction-force counterpart.
Centrifugal force
When no external torque acts on an object or a system of objects, no change of angular momentum can occur. Hence, the angular momentum before an event involving only internal torques or no torques is equal to the angular momentum after the event.
Conservation of angular momentum
Door B is twice as wide as door A, but both doors have the same height and the same mass. A person pushes on the edge of the two doors with the same force. Which door opens more quickly?
Door A
When a rock tied to a string whirled in a horizontal circle somehow doubles in mass but keeps the same speed, the string tension
Doubles
Your pet hamster sits on a record player whose angular speed is constant. If he moves to a point twice as far from the center, then his linear speed...
Doubles
Which is easier to get swinging, a baseball bat held at the end or one held closer to the massive end (choked up)?
Easier to swing the bat holding it closer to the big end
As a car speeds up when rounding a curve, does the centripital force on the car also increase? Defend your answer.
Yes. F=mv^2/r
Consider someone in a rotating space habitat. Rotational motion provides _______.
a support force
When a train makes a curve, a tapered wheel rim is able to A) cover different distances per revolution. B) maintain a fixed rotational speed. C) reduce differences in angular speeds.
cover different distances per revolution.
Each rolling wheel of a railroad train is tapered. Compared with the wide part, the narrow part of the wheel has a tangential speed that is A) less. B) greater. C) the same for both.
less.
As the polar icecaps melt, the resulting water spreads over the entire Earth. This new mass distribution tends to make the length of a day
longer.
Put a pipe over the end of a wrench when trying to turn a stubborn nut on a bolt, to effectively make the wrench handle twice as long, you'll multiply the torque by
two
A flywheel's diameter is twice that of another of the same shape and mass. Rotational inertia of the larger flywheel is A) two times greater. B) four times greater. C) the same as the other's.
two times greater.
Which horse moves faster in m/s on a merry-go-round?
one near outer rail
Which will roll down an incline in the shortest time, a can filled with water or the same can filled with ice? -ice -water -both the same -Not enough information is given.
water Because the molecules in ice are more spread out they will have a higher amount of rotational inertia causing the the can to role slower if it were water because the the H2o molecules are closer together.
Just as an external net force is required to change the linear momentum of an object, an external net torque is required to change the angular momentum of an object. We can state a rotational version of Newton's first law (the law of inertia):
An object or system of objects will maintain its angular momentum unless acted upon by an external net torque.
A ball rolls down a hill mainly because of...
An unbalanced torque
When a car drives off a cliff it rotates forward as it falls. For a higher speed off the cliff, discuss whether the car will rotate more or less.
It will rotate with a greater angular velocity when it is travelling slowly. When the front of the car is just over the edge, the car will not rotate as the center of mass is still above ground, thus negates gravity's torque.
How is a flywheel constructed to maximize its rotational inertia?
Most of the mass is concentrated far from the axis.
at the center of the disk
The center of gravity of a circular disk of sheet metal is
Why must you bend forward when carrying a heavy load on your back?
You change your center of gravity to keep balanced
An industrial flywheel has a greater rotational inertia when most of its mass is A) nearer the rim. B) nearer the axis. C) uniformly spread out as in a disk.
nearer the rim.
The rotational inertia of a pencil is greatest about an axis A) along its length, where the lead is. B) about its midpoint, like a propeller. C) about its end, like a pendulum.
about its end, like a pendulum.
The famous Leaning Tower of Pisa doesn't topple over because its center of gravity is -stabilized by its structure. -above a place of support. -in the same place as its center of mass. -relatively low for such a tall building. -displaced from its center.
above a place of support Justification: If a line is drawn straight down from the center of gravity of an object and it falls within the inside of it's base, then it is with in equilibrium. Meaning it will stay balanced in this state. This is what is occurring with the tower of Pisa
A baseball bat is balanced on a fulcrum. The center of gravity of the bat is located -near the heavy end. -above the fulcrum. closer to the handgrip.
above the fulcrum Justification: Because the fulcrum is always located below the center of gravity.
A ball gains speed while rolling down a hill due mainly to A) its rotational inertia. B) its angular acceleration. C) a balanced torque. D) an unbalanced torque.
an unbalanced torque.
Multiple the equation for linear momentum by radial distance r and you have
angular momentum.
If Earth had a pair of identical moons on opposite sides of the same circular orbit, the center of gravity of the double-moon-Earth system would be
at the center of the Earth.
A vertically-held sledge hammer is easier to balance when the heavier end is A) on your hand. B) at the top, away from your hand. C) the same either way
at the top, away from your hand.
The tapered shape of the wheel rims that ride on railroad tracks allows opposite wheels to A) in effect, vary their diameters. B) travel at different linear speeds for the same rotational speed. C) both of these
both of these
A ball that gains speed as it rolls down a hill experiences a
net torque. net force. both of these
When the rotational speed of a rotating system doubles, its angular momentum _______.
doubles
A tightrope walker more easily balances on a tight wire if her pole A) is held high. B) droops. C) is short but heavy.
droops.
Consider two flywheels of the same size and shape, but one with twice the mass. Rotational inertia of the more massive one is A) two times greater. B) four times greater. C) half.
four times greater.
Consider a string with several rocks tied along its length at equally spaced intervals. You whirl the string overhead so that the rocks follow circular paths. Compared with a rock at the end of the string, a rock at the middle moves A) half as fast. B) twice as fast. C) at the same linear speed.
half as fast.
A boy plays solitary seesaw by placing the seesaw's fulcrum one-eighth the distance from where he sits at one end. Which weighs more? A) the boy B) the seesaw C) they have equal weights D) need more information
the boy
To kick a football so it won't topple end over end, kick it so the force of impact extends
through its center of gravity
A large wheel is coupled to a wheel with half the diameter, as shown in the sketch. How does the rotational speed of the smaller wheel compare with that of the larger wheel? Discuss the comparisions of the tangential speeds at a rims.
...
Earth is not spherical but bulges at the equator. Jupiter bulges more. What is the cause of these bulges?
...
How can the three bricks be stacked so that the top brick has maximum horizontal displacement from the bottom brick? For example, stacking them as suggested by the dashed lines would be unstable and the bricks would topple.
...
Most often we say that force cause acceleration. But when Evan took a ride in a rocket sled at Bonneville Salt lats, blood was forced to the back of his brain, nearly blacking him out. Discuss and identify the cause of this force.
...
Use the equation v=rw to explain why the end of a flyswatter moves much faster than your wrist when you swat a fly.
...
With respect to Diana's finger, where is the center of mass of the platic bird? Discuss how this balance can be accomplished during its manufacture.
...
A 1-kg rock is suspended from the tip of a horizontal meterstick at the 0-cm mark so that the meterstick barely balances like a seesaw when its fulcrum is at the 25-cm mark. From this information, the mass of the meterstick is
1 kg
A 1-kg rock is suspended from the tip of a meter stick at the 0-cm mark so that the meter stick balances like a seesaw when the fulcrum is at the 25-cm mark. From this information, what is the mass of the meter stick? -1/2 kg -1/4 kg -3/4 kg -1 kg -more than 1 kg
1 kg
A girl weighs 60 pounds and is sitting on the teeter-totter 3 m from the center. How far from the center should a 180-pound boy sit so that the teeter-totter balances?
1 meter
To tighten a bolt, you push with a force of 84N at the end of a wrench handle that is 0.20m from the axis of the bolt. What torque are exerting? If you move your hand inward to be only 0.10 m from the bolt, find the force that you should exert to achieve the same torque.
17 N*m 170 N (Answers depend on direction of your push relative to the direction of the wrench handle)
The circumference of a bicycle wheel is 2 meters. If it rotates at 1 revolution per second then its linear speed is
2 m/s.
Calculate the torque produced by a 60-N force when a pipe extends the length of the wrench to 0.60 m .
36Nm
A racing car on a flat circular track needs friction between the tires and the track to maintain its circular motion. How much more friction is required for twice the speed?
4 times the force.
The circumference of a bicycle wheel is 2 meters. If it rotates at 1 revolution per second then its linear speed is A) 1 m/s. B) 2 m/s. C) 3 m/s. D) 3.14 m/s. E) 6.28 m/s.
6.28 m/s.
If you're on a Ferris wheel at a carnival, seated 10 m from the Ferris wheel's axis that makes a complete rotation each minute, your linear speed is A) 10 m/min. B) 31.4 m/min. C) 62.8 m/min. D) 100 m/min.
62.8 m/min.
What is the law of inertia for rotating systems in terms of angular momentum?
Angular momentum does not change without an applied external torque.
Linear momentum = mass × velocity
Angular momentum's counterpart is:
You can swing your legs to and fro more frequently when your legs are A) straight. B) bent. C) same either way
B) bent.
Stand a broom upright on the end of its pole and let it topple to the floor. Repeat, but with the bristles end on the floor. The faster fall will be the broom standing on its A) pole-end. B) bristles-end. C) the same either way
B) bristles-end.
You hold a meterstick at one end with the same mass suspended at the opposite end. Rank the torque needed to keep the stick steady, from largest to smallest
BCA
Why are lightweights tires perferred in bicycle racing? Discuss and explain
Because of inertia. Heavier wheels are harder to get spinning than lighter wheels.
Why does bending your legs when running enable you to swing your legs to and fro more rapidly?
Bending your legs shortens them, thus reducing rotational inertia.
If a skater who is spinning pulls her arms in so as to reduce her rotational inertia by half, by how much will her angular momentum increase? By how much will her rate of spin increase?
By pulling in her arms, R becomes ½R mvR (before)=m(2v)(½R)[after] V(rate of spin) after must be double in order to conserve angular momentum
Three types of roller are placed on slightly inclinded parallel meterstick tracks as shown. From greatest to least, rank the rollers in terms of their ability to remain stable as they roll.
C, A, B
Calculate the tension in a horizontal string that whirls a 2.2-kg toy in a circle of radius 2.5m when it moves at 3.4m/s on an icy surface.
F =10 N
When a bowling ball leaves your hand, it may not spin. But farther along the alley, it does spin. What produces the spinning?
Friction between the ball and the lane.
How can gravity be simulated in an orbiting space station?
Gravity can be stimulated by rotating a space station
If a skater who is spinning pulls her arms in so as to reduce her rotational inertia by half, by how much will her angular momentum change? By how much will her rate of spin change?
Her angular momentum does not change. Her spin rate doubles.
If the string that holds a whirling can in its circular path breaks, what kind of force causes it to move in a straight-line path--centripetal, centrifugal, or no force? What law of physics supports your answer?
If the string holding the whirling can breaks centrifugal force(the can's inertia) makes it fly off in a straight line
The spool is pulled in three ways, as shown. There is sufficient friction for rotation. In what direction will the spool roll in each case? Discuss and explain.
In all three cases the spool moves to the right. In the first case there is a torque about the point of contact with the table that rotates the spool clockwise, so the spool rolls to the right. In the second case the pull's line of action extends through the point of table contact, yielding no lever arm and therefore no torque; but with a force component to the right; hence the spool slides to the right without rolling. In the third case the torque produces clockwise rotation so the spool rolls to the right.
What is the relationship between center of gravity and support base for an object in stable equilibrium?
In stable equilibrium the center of mass of the object is over its base of support
When you pedal a bicycle, maximum torque is produced when the pedal sproket arms are in the horizontal position, and no torque is produced when they are in the vertical position. Explain
In the horizontal position the lever arm equals the length of the sprocket arm, but in the vertical position, the lever arm is zero because the line of action of forces passes right through the axis of rotation
Friction is needed for a car rounding a curve. But, if the road is banked, friction may not be required at all. What, then, supplies the needed centripetal force?
It has a horizontal component that provides the centripital force.
Why is centrifugal force in a rotating frame called a "fictitious force"?
It is not a fundamental force of nature. Instead, it is a force that only appears in an accelerating frame of reference.
What is meant by the "lever arm" of a torque?
It is the perpendicular distance from the rotational axis to the line along which the force acts.
If you toss a stick into the air, it appears to wobble all over the place. Specifically, about what place does it wobble?
It will rotate about the center of mass.
If the world's populations moved to the North Pole and the South Pole, would the 24 hour day become longer shorter, or stay the same?
It would be slightly shorter. Rotational speed increases.
Joe lives on the equator, and Sally lives in Alaska. Which person has the higher speed due to Earth's rotation?
Joe B/C - The equator is further from the axis of rotation than Alaska.
Calculate the angular momentum of the person if the force of friction that keeps a 90-kg person sitting on the edge of a horizontal rotating platform when the person sits 2.1m from the center of the platform and has a tangential speed of 4.0m/s .
L = 760 kg⋅m2s
Distinguish between linear momentum and angular momentum.
Linear momentum is in a straight line and depends on the objects mass and velocity. Angular (rotational) momentum depends on the objects mass, velocity, and radius.
A small boy places a rock under the middle of a of a long wood plank, sits near one end and his mother sits near the opposite end. To balance each other -both should move closer to the ends of the plank. -the mother should move further away from the boy. -the boy should move closer to his mother. -both should move closer to the middle of the plank. -None of the above choices would work.
None of the above choices would work. Justification: The heavier mother should move closer to HER LIGHTER SON since he's putting less force on the seesaw, and she's putting more she need to lower the length of her torque arm by moving closer to the fulcrum
While riding on a carnival Ferris wheel, Sam Nasty horses around and climbs out of his chair and along the spoke so that he is halway to the axis. How does his rotational speed compare with that of his friends who remain in the chair? How does hi tangentital speed compare? Why are your answers different?
Rational speed will be the same because it is powered. Tangenital speed will be 1/2 because the radial distance is half. They're different because tangential speed is not the same as rotational speed.
If all of Earth's inhabitants moved to the equator, how would this affect Earth's rotational ineratia? How would it affect the length of a day?
Rotational inertia would increase. The day would be longer and the spin would slow.
Why is it easier to carry the same amount of water in two buckets, one in each hand, than in a single bucket>
So you are balanced. Your Center of gravity is in the center of the support base so you don't have to lean.
remains the same, but the RPMs decrease
Suppose you are at the center of a large freely-rotating horizontal turntable in a carnival funhouse. As you crawl toward the edge, the angular momentum of you and the turntable
Using the ideas of torque and center of gravity, explain why a ball rolls down a hill.
The Center of gravity of a ball is not above a point of support when the ball is on an incline. The weight acts at some distance from the point of support which is like a fulcrum. The torque is produced and the ball rotates.
Where is the center of mass of a baseball? Where is its center of gravity? Where are these centers for a baseball bat?
The center of mass of a baseball is at the center. The center of gravity of a baseball is at the center. The center of mass and gravity for a baseball bat are closer to the bat head where there is more mass.
Is it an inward force or an outward force that is exerted on the clothes during the spin cycle of an automatic washing machine? What about the direction of the force on the water?
The force is inward on clothes and there is none on water.
Why does a typical small helicopter with a single main rotor have a second small rotor on its tail? Describe the consequence if the small rotor fails in flight.
The helicopter and main rotor would rotate in the opposite directions. The smaller rotor provides a torque to offset the rotational motion that the helicopter would otherwise have.
Tangential speed
The linear speed tangent to a curved path, such as in circular motion.
Discuss how a ramp would help you to distinugish between two identical looking spheres of the same weight, one solid and the other hallow.
The moment of inertia of a hallow sphere is greater than the solid sphere and so it rolls down slowly.
Is the net torque changed when a partner on a seesaw stands or hangs from her end instad of sitting. (Does the weight or the lever arm change?
The net torque stays the same. The lever arm will stay the same whether a person stands, sits or hangs from the end.
Rotational speed (sometimes called angular speed)
The number of rotations or revolutions per unit of time; often measured in rotations or revolutions per second or per minute. (Scientists usually measure it in radians per second.)
How does the tapered rim of a wheel on a railroad train allow one part of the rim to have a greater tangential speed than another part when it is rolling on a track?
The tangential speed is proportional to the radius. The inside of the wheel rolls on a larger radius than the outside of the wheel.
A tapered cup rolled on a flat surface makes a circular path. What does this tell you about the tangential speed of the rim of the wide end of the cup compared with that of the rim of the narrow end?
The tangential speed of the wide end is faster.
Flamingos are frequently seen standing on one leg with that other leg lifted. Is rotational inertia enhanced with long legs? What can you say about the bird's center of mass with respect to the flot on which it stands?
Their center of mass is higher and their foot is directly below their center of mass. Rotational inertia is enhanced.
Explain why a centripetal force does not do work on a circularly moving object.
There is no component of force parallel to the direction of motion which work requires
If you are not wearing a seat belt in a car that rounds a curve, and you slide across your seat and slam against a car door, what kind of force is responsible for your slide: centripetal, centrifugal, or no force?
There is no force as viewed by someone outside the car. To them you move in a straight line.
How do clockwise and counterclockwise torques compare when a system is balanced?
They are equal in magnitude and opposite in direction.
What does a torque tend to do to an object?
Torque tends to twist or change the state of rotation of the object.
Assuming your feet are not held down, which is more difficult: doing sit-ups with your knees bent or with your legs straight out.
When your legs are straight out, your center of gravity is further away and you have to work harder to sit up. more torque.
Centripetal force does no work on a circularly-moving object because
centripetal force has no component in the direction of motion.
The center of mass of a human body is located at a point that
changes as a person bends over.
A coin and a ring roll down an incline starting at the same time. The one to reach the bottom first will be the -ring. -coin. -Both reach the bottom at the same time.
coin. Justification: This is because the coins mass is less spread out among itself, opposed to the ring that has all of its mass spread out and concentrated on its outer parts away from its center of gravity. This gives the ring a greater rotational inertia, so it takes the ring while to gain speed because objects that have a large amount of inertia resist change in motion.
Tangential speed is directly proportional to rotational speed at every fixed distance that from the axis of rotation. For example, on a merry go round, the faster its rotational speed the faster the tangential speed of any person on the ride.
hat is the relationship between tangential speed and distance from the center of the rotational axis? Give an example.
A broom is easier to balance on its end when the heavier end (the brush end) is -nearest your hand. -highest, farthest from your hand. -same either way
highest, farthest from your hand. Justification: Because with the heavier weight of the broom father away from your hand, this gives the broom more rotational inertia. This prevents the broom from rotating off your finger as easily, because it has more of the property to resist change.
If the rotational speed of a rotating habitat in space increases, the weight experienced by occupants
increases
Stand a meterstick on its end and let it rotate to the floor. If you attach a heavy glob of clay to its upper end and repeat, the time to fall will be A) shorter. B) longer. C) the same.
longer.
Consider a ball rolling around in a circular path on the inner surface of a cone. The weight of the ball is shown by the vector W. WIthout friction only one other force acts on the ball. a normal force. A. Draw a vector for the normal force. b. Using the parallelogram rule, show that the rsultant of the two vectors is along the radial direction of the ball's circular path.
look at notes
The sketch shows a coin at the edge of a turntable. The weight of the coin is shown by a vector W. Two other forces act on the coin-the normal force and force of friction that prevents it from sliding off the edge. Draw force vectors for both of these.
look at notes
A solitary boy cannot balance on a seesaw with its fulcrum at its midpoint. If the fulcrum is moved to one-quarter the distance from the boy, balance is achieved when the weight of the boy is A) less than the weight of the seesaw. B) equal to the weight of the seesaw. C) more than the weight of the seesaw. D) need more information
more than the weight of the seesaw.
Which of these animals has a quicker stride? A) giraffe B) horse C) cat D) mouse
mouse
Horses with the greatest linear speed on a merry-go-round are located A) near the center. B) near the outside. C) anywhere, because they all move at the same speed.
near the outside.
Which moves faster in m/s on a merry-go-round: a horse on the inside or a horse on the outside near the outer rail? -inside horse -outside horse -Both move at the same speed in m/s.
outside horse Justification: This is because a point farther from the center travels a longer path in the same time and therefore has a greater tangential speed.
A ring and a disk both at rest roll down a hill together. Which rolls slower? A) ring B) disk C) both roll at the same speed
ring
Two people are balanced on a seesaw. If one person leans inward toward the center of the seesaw, that person's end of the seesaw tends to A) rise. B) fall. C) stay at the same level. D) need more information
rise.
When railroad tracks make a curve, the outer track is longer. This means a wheel that rides on the outer track needs to somehow A) roll slower than the wheel on the inner track. B) maintain the same speed as the wheel on the inner track. C) roll faster than the wheel on the inner track.
roll faster than the wheel on the inner track.
A huge rotating cloud of particles in space gravitate together to form an increasingly dense ball. As it shrinks in size, the cloud rotates faster. cannot rotate. rotates at the same speed. rotates slower.
rotates faster. Justification: By coming together the particles are lowering the rotational inertia. And according to according to the law of conservation of angular momentum, the lowering of rotational inertia raises rotational velocity.
Centrifugal forces are an apparent reality to observers in a reference frame that is
rotating
Compared with a force, a torque involves
rotation. leverage. distance from an axis of rotation. all the above
Spinning motion that occurs when an object rotates about an axis located within the object (usually an axis through its center of mass).
rotational
The rotational inertia of your leg is greater when your leg is A) straight. B) bent. C) same either way
straight.
Which jar will roll down an incline in the shortest time, an empty one or one filled with peanut butter? A) the empty jar B) both reach the bottom at the same time C) the filled jar
the filled jar
The centers of gravity of the three trucks parked on a hill are shown by the Xs. Which truck(s) will tip over? -the left truck -the middle truck -the right truck
the left truck Justification: If a line is drawn straight down from the center of gravity of an object and it falls within the inside of it's base, then it is with in equilibrium. Meaning it will stay balanced in this state.
You can safely stand on the overhanging end of a heavy plank that rests on a table. How much overhang depends on your mass and the plank's mass. If you can stand on the end of a plank that overhangs the edge of the supporting table 1/4 its total length, how massive is the plank compared to your mass?
the same
A carnival has a Ferris wheel where the seats are located halfway between the center and outside rim. If you were at the outside rim, your angular speed while riding on this Ferris wheel would be
the same and your tangential speed more
If Alex wishes to rotate his skateboard, then he must apply a A) torque. B) rotational maneuver. C) pause before bearing down on the board.
torque.
If you place a pipe over the end of a wrench when trying to rotate a stubborn bolt, effectively making the wrench handle twice as long, you'll multiply the torque by
two
A flywheel's mass is twice that of another of the same size and shape. The more massive flywheel's rotational inertia is -the same as the other's. -two times the other's. -four times the other's. -half the other's.
two times the other's Justification: Since the second flywheel is twice the size of the first then it has twice the amount of mass. Even though it is the same size and shape, mass is the measurement of inertia. This means that the second flywheel has more rotational INERTIA
To rotate a stubborn screw, it is best to use a screwdriver that has a A) wide handle. B) long handle. C) smooth handle. D) none of the above
wide handle.
Tangential speed~
~radial distance × rotational speed. In symbol form, v ~ rω
Calculate the torque produced by a 52-N perpendicular force at the end of a 0.20-m-long wrench.
τ =10 Nm
As you crawl toward the edge of a large freely-rotating horizontal turntable in a carnival funhouse, the angular momentum of you and the turntable
remains the same, but the revolutions per minute decrease.
Motion of an object turning around an axis that lies outside the object.
revolution
A torque acting on an object tends to produce -a center of gravity. -rotation. -linear motion. -velocity. -equilibrium.
rotation Justification: Torque is the rotational counterpart of *force*. So since force changes the motion of an object, Torque is just the name for the amount of force that changes the *rotational motion* of an object.
Angular momentum is defined as the product of rotational inertia and rotational velocity. Like linear momentum, angular momentum is a vector quantity and has direction as well as magnitude. Angular momentum =
rotational inertia × rotational velocity
Which will have the greater acceleration rolling down an incline: a hoop or a solid disk? Why?
The solid disk will because the mass is closer to the axis of rotation.
Equilibrium
The state of an object in which it is not acted upon by a net force or a net torque.
A ring, a disk, and a solid sphere begin rolling down a hill together. The one to reach the bottom first is the -sphere. -ring. -disk. -They all reach the bottom at the same time. -Not enough information is given.
sphere Justification: This is because the sphere's mass is the least spread out among itself, opposed to the ring and the disk that have all of their mass spread out and concentrated on its specific parts away from its center of gravity. This gives the sphere a least rotational inertia, so it takes the ring the least time to gain speed because objects that have a large amount of inertia resist change in motion.
To turn a stubborn screw, it is best to use a screwdriver that has a long handle. wide handle. smooth handle. none of these
wide handle Justification: According to Diameter × Force =Torque. Diameter is inversely proportional to force, so the the wider the lever arm, in this case the handle of the screwdriver, the lower the force has to be.
The rotational inertia of a pole, or of any object, depends on the axis about which it rotates.⁴
⁴When the mass of an object is concentrated at the radius r from the axis of rotation (as for a simple pendulum bob or a thing ring), rotational inertia I is equal to the mass m multiplied by the square of the radial distance. For this special case, I = mr².
(a) Straight line about which rotation takes place. (b) Straight lines for reference in a graph, usually the x-axis for measuring horizontal displacement and the y-axis for measuring vertical displacement.axis
(pl. axes)
Re call the equilibrium rule in Chapter 2--that the sum of the forces acting on a body or any system must equal zero for mechanical equilibrium. That is, ∑F = 0. We now see an additional condition. The *net torque* on a body or on a system must also be zero for mechanical equilibrium...
...(∑T = 0, where T stands for torque). Anything in mechanical equilibrium doesn't accelerate--neither linearly nor rotationally.
On a balanced seesaw, a boy three times as heavy as his partner sits -more than 1/3 the distance from the fulcrum. -1/3 the distance from the fulcrum. -less than 1/3 the distance from the fulcrum.
1/3 the distance from the fulcrum*. Justification: This is because Lever arm × Force =Torque. So since the boy is 3 times heavier he's putting 3 times the force on the lever, which equals to a higher torque according to the equation. To balance the seesaw with the other boy who's putting less 3 times less force on it, he has to sit 1/3 closer to the fulcrum. Because the farther he's from the fulcrum the higher the integer that needs to be entered into the lever arm part of the equation.
You can safely stand on the overhanging end of a heavy plank that rests on a table. How much overhang depends on your mass and the mass of the plank. If you can stand on the end of a plank that overhangs the edge of the supporting table 1/5 its total length, how massive is the plank compared to your mass?
2/3
The product of a body's rotational inertia and rotational velocity about a particular axis. For an object that is small compared with the radial distance, it can be expressed as the product of mass, speed, and the radial distance of rotation.
Angular momentum
For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as the magnitude of its linear momentum, *mv*, multiplied by the radial distance, *r*. In shorthand notation:
Angular momentum = mvr (also = Iω)
The center of gravity of a circular disk of sheet metal is...
At the center of the disc
Consider three axes of rotation for a pencil: along the lead, at right angles to the lead at the middle, and at right angles to the lead at one end. Rate the rotational inertias about each axis from smallest to largest.
Axis along the lead, through the center, through one end
What is required to change the angular momentum of a system?
External torque
Calculate the tension in a horizontal string that whirls a 1.8-kg toy in a circle of radius 2.5m when it moves at 2.8m/s on an icy surface.
F = 5.6 N B/C - Centripetal force = F=mv^2/r
the resultant forces and torques must both be zero. Justification: For something to be in MEchanical equilibrium then all forces must cancel out in to zero. and torque is just rotational force, another force that must be at zero
For a system in mechanical equilibrium -the resultant forces and torques must both be zero. -the resultant torques must be zero. -the resultant forces and torques must be equal. -the resultant force must be zero.
The torque exerted by a crowbar on an object increases with increased...
Force and leverage distance
Suppose Sally lived on the equator of a planet that had a radius twice that of Earth's radius and that rotated with twice the angular velocity (so one day would be 12 hours long). Sally's speed on this planet would be _______ Joe's speed (who lives on Earth's equator).
Four times faster than B/C - Sally's angular velocity is twice as high as Joe's, and since Sally is tracing out a circle with twice the radius of Joe's path, Sally is going four times faster than Joe.
The tangential speed on the outer edge of a rotating carousel is...
Greater than toward the center
near the outside Justification: This is because a point farther from the center travels a longer path in the same time and therefore has a greater tangential speed.
Horses that move with the fastest linear speed on a merry-go-round are located -near the outside. -anywhere, because they all move at the same speed. -near the center.
double Justification: This is because rotational speed is directly proportional to tangential speed. Although the linear speed of an object moving in a circular path, (which is tangential speed) is relative to its location at each point. Any time the rotational speed changes it effects the tangential speed. Which in this case would be the speed of the hamster
If a turntable's rotational speed is doubled, then the linear speed of a pet hamster sitting on the edge of the record will -double. -halve. -remain the same.
number of rotations or revolutions per unit of time
It is common to express rotational rates in revolutions per minute (RPM).
As distance increases between most of the mass of an object and its center of rotation, how does rotational inertia change?
It increases.
Is it easier for a circus performer to balance a long rod held vertically with people hanging off the other end, or the same long rod without the people at the other end, and why?
It is easier for the performer to balance a long rod held vertically with people at the other end because the rotational inertia is greater.
Is it easier to balance a long rod with a mass attached to it when the mass is closer to your hand or when the mass is farther away?
It is easier when the mass is farther from your hand.
If the string that holds a whirling can in its circular path breaks, what kind of force causes it to move in a straight- line path: centripetal, centrifugal, or no force? What law of physics supports your answer?
No force; Newton's first law
When a rock tied to a string is whirled in a horizontal circle, doubling the speed...
Quadruples the tension in the string
Physics types usually describe rotational speed, ω, in terms of the number of "radians" turned in a unit of time. There are a little more than 6 radians in a full rotation (2π radians, to be exact). When a direction is assigned to rotational speed, we call it rotational velocity). Rotational velocity is a vector whose magnitude is the rotational speed. By convention, the rotational velocity vector lies along the axis of rotation.
RPM
Suppose you are at the center of a large freely-rotating horizontal turntable in a carnival funhouse. As you crawl toward the edge, the angular momentum of you and the turntable...
Remains the same, but the RPMs decrease.
Why does the rotational inertia of the rod with the attached mass closer to your hand compare the way it does with the rotational inertial of the rod with the attached mass farther away?
Rotational inertia depends on whether the mass is farther or closer to the point of rotation. The farther the mass is, the higher the rotational inertia.
smaller than that of the wide part Justification: This is because a point closer to the center travels a shorter path in the same time and therefore has a smaller tangential speed.
Since each rolling wheel of a railroad train is tapered, the narrow part of the wheel has a tangential speed that is -greater than that of the wide part. -the same as that of the wide part. -smaller than that of the wide part.
If you hang at rest by your hands from a long vertical rope, where is your center of gravity with respect to the rope?
Somewhere straight below where your hands grab the rope
On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?
Tangential speed increases with distance. Rotational speed is constant.
A ring and a disk, initially at rest, roll down a hill together. The one to reach the bottom first...
The disk
Neglecting air resistance, which will roll from rest to the bottom of an incline first, an empty jar, or the same jar filled with peanut butter?
The filled jar
Consider three axes of rotation for a pencil: along the lead; at right angles to the lead at the middle; at right angles to the lead at one end. Rate the rotational inertias about each axis from small to large.
The first is at the central core parallel to the length of the pencil, where the lead is. The second is perpendicular to the midpoint of the pencil; and the third axes is perpendicular to one end of the pencil. Rotational inertia is very small at the first position, and it's easy to rotate the pencil between your fingertips because most of the mass is very close to the axis of the pencil. The second axis, is greater because it's weight is distributed more. The third axis, which is at the end of the pencil swings like a pendulum, rotational inertia is even greater than the second axis.
Torque
The product of force and lever-arm distance, which tends to produce rotation. Torque = lever arm × force
Rotational inertia (often called moment of inertia)
The property of an object that measures its resistance to any change in its state of rotation: if at rest, the body tends to remain at rest; if rotating, it tends to remain rotating and will continue to do so unless acted upon by a external net torque.
How does the rotational inertia of the rod with the mass toward the bottom compare with the rotational inertia of the mass toward the top?
The rotational inertia of the rod with the mass closer to the top is greater than the rotational inertia of the rod with the mass closer to the bottom.
When you whirl a can at the end of a string in a circular path, what is the direction of the force you exert on the can?
Toward the center of the circle
How do clockwise and counterclockwise torques compare when a system is balanced?
When Clockwise moment is equal to the anti-clockwise moment they have about the same torque, and remain in equilibrium. This is because both torque cancel each other out.
when all wheels are on the ground, the car's center of gravity is above a support base. But, when the car drives off a cliff, the front wheels are first to leave the ground and the support base shrinks to the line between the rear wheels. So the car's center of gravity extends beyond the support base and it rotates.
When a car drives off a cliff it rotates forward as it falls. For a higher speed off the cliff, will it rotate more, or less? (Consider the time that the unbalanced torque acts.)
balled up Justification: Angular momentum = rotational inertia X Rotational velocity (according to the equation) This means when rotational inertia goes down, then rotational velocity goes up. In Other words when you bring your arms and legs into lower rotational velocity, then you will spin faster because your rotational velocity will go up
When doing somersaults, you'll more easily rotate when your body is straight with both arms at your sides. balled up. straight with both arms above your head. no difference
This is due to Centrifugal force which is not a "real" force. The force that you feel while being pressed against the door is due to your inertia as the car turns. According to Newton's third law an object in motion tends to stay in motion. So your body keeps going in one direction, while the car moves in another pushing the car door against you. The car door provides a centripetal force to make you turn.
When you are in the front passenger seat of a car turning to the left, you may find yourself pressed against the right-side door. Why do you press against the door? Why does the door press on you? Does your explanation involve a centrifugal force, or Newton's laws?
If you balance a broom horizontally on one finger, the center of gravity of the broom will be above your finger - closer to the bristles end than the handle end. If you saw the broom in two pieces at that point and weigh the two parts on a scale, you'll find that the heavier part is the -bristles part. -handle part. -both the same weight
bristles part Justification: Justification: This is because Lever arm × Force =Torque. The center of gravity where the fulcrum was located was there to compromise for the extra weight of the bristle and so, it's lowering the lever arm there. like the fat kid on the seesaw. SO if you cut the broom in half there, the bristle end will still be heavier.
The long, heavy tail of a spider monkey enables the monkey to easily vary its -inertia. -weight. -center of gravity. -momentum. -none of these
center of gravity: Justification: A rigid object only has one center of gravity. A non-rigid object such as a monkey that can move also can only have one center of gravity, but depending on the way the monkey changes its position or shape, that center its center of gravity can be repositioned. Like in the case with it's tail.
Toss a baseball bat into the air and it wobbles about its -heavier end. -geometrical center. -center of mass.
center of mass When an object is thrown in the air symmetrical or not, the weight around it always moves around its center of mass. So when a baseball bat is thrown in the air although it look like its wobbling all over the place its center of mass stays around the same place while its following its trajectory.
The chef at the infamous Fattening Tower of Pizza tosses a spinning disk of uncooked pizza dough into the air. The disk's diameter increases during the flight, while its rotational speed -increases. -remains constant. -decreases.
decreases Justification: This is because as the disk is getting larger it's spreading it mass farther and farther out. This means its gaining more rotational inertia. Therefore the pizza disc beginning to resist change and is decreasing in speed.
A car travels in a circle with constant speed. The net force on the car is -directed toward the center of the curve. -directed forward, in the direction of travel. -zero because the car is not accelerating. -none of these
directed toward the center of the curve. Justification: Any force directed toward a fixed center is *centripetal force* and in the case of this car, as long as the car in a circle with constant speed like bucket on a string around their head then the n there is a force constantly pulling the car inward toward the center, just like the string of the bucket.
Your pet hamster sits on a record player that has constant angular speed. If the hamster moves to a point twice as far from the center, then its linear speed
doubles
Centripetal force
force A force directed toward a fixed point, usually the cause of circular motion : F = mv²/r.
A flywheel's diameter is twice that of another of the same shape and mass. Rotational inertia of the larger flywheel is
four times greater.
If the planet Jupiter underwent gravitational collapse, its rate of rotation about its axis would increase. decrease. stay the same. more information needed
increase Justification: Angular momentum = rotational inertia X Rotational velocity (according to the equation) This means when rotational inertia goes down, then rotational velocity goes up. So as jupiter's mass becomes less spread out, it rotational inertia goes down, and this in turn raised its rotational velocity.
If the Earth rotated more slowly about its axis, your apparent weight would -stay the same. -increase. -be zero. -decrease.
increase Justification: When the Earth is spinning, we experience a centrifugal force that slightly decreases are weight, it slightly pushes us away from earth. if the Earth were to slow down then this force would decrease and we would increase weight.
Rotational inertia about the midpoint of an object becomes greater with _______.
increased mass and increased distance to mass concentration
When a twirling ice skater brings her arms inward, her rotational speed -decreases. -remains the same. -increases.
increases Justification: according to the law of conservation of angular momentum, If no external net torque acts on a rotating system, then the angular momentum of the system remains the same. in this case the ice skater changes the net torque of her rotating system by lowering her rotational inertia when she brings her arms in, this raises her rotational velocity .
What are the units of measurement for tangential speed? For rotational speed?
m/s for tangential, RPM for rotational
A 1-kg rock is suspended from the tip of a horizontal meterstick at the 0-cm mark so that the meterstick barely balances like a seesaw when its fulcrum is at the 12.5-cm mark. From this information, the mass of the meterstick is
none of the above
Calculate the torque produced by a 42-N perpendicular force at the end of a 0.25-m-long wrench.
r = 11 Nm B/C - Torque = Level arm * Force