Physics Chapter 8
How can gravity be simulated in an orbiting space station?
-Rotate a cylinder to create centrifugal force as viewed by a person on the inside of the curved outer wall -Spin a station shaped like a bicycle wheel -Spin two pods connected by a cable
Compared with a force, a torque involves
-leverage -rotation -distance from an axis of rotation
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 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 Since the boy weighs three times more than the girl, he needs to be only one-third the distance from the center in order for the torque he exerts on the teeter-totter to balance that of the girl
On a balanced seesaw, a boy three times as heavy as his partner sits
1/3 the distance from the fulcrum
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
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
62.8 m/min
Suppose we replace the mass in the video with one that is four times heavier. How far from the free end must we place the pivot to keep the meter stick in balance?
90 cm (10 cm from the weight)
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
Distinguish between linear momentum and angular momentum
Angular momentum depends on the distribution of mass, whereas linear momentum depends on the total mass
What is the law of inertia for rotating systems in terms of angular momentum?
Angular momentum does not change without an applied external torque
A baseball bat can be rotated around many different axes of rotation. Three such possibilities are shown in (Figure 1) . Rank the baseball bat's moment of inertia about each of these three axes of rotation
B, A, C Because the total mass is the same for all three axes, only the distribution of that mass changes the moment of inertia. All of the mass is close to axis C, so that the axis has the smallest moment of inertia. The bulk of the mass (in the meat of the bat) is further from axis B than A; therefore, axis B has the largest moment of inertia
Given the same baseball bat and possible axes of rotation shown in (Figure 1) , for which axis of rotation would it be the easiest to rotate the bat from rest?
C (the end) The smaller the moment of inertia of an object, the easier it is to change its state of rotation
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 Even though the torque applied on door A is half that of door B, the moment of inertia of door B is four times higher than that of door A (the moment of inertia is proportional to the square of the width of the door)
What is required to change the angular momentum of a system?
External torque
Calculate the tension in a horizontal string that whirls a 1.9-kg toy in a circle of radius 2.0 m when it moves at 2.9 m/s on an icy surface
F= 7.98N Centripetal Force: F=mv^2/r
Shown in the figure is a view of a door from above. Three forces are shown acting on the door. Which force is causing the largest torque on the door?
Force A The torque of force A is 150 N⋅ m(τ=Fr=(300 N)(0.5m)=150 N)
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 Since 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
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
How does the force needed to turn the wrench change if you increase the lever arm?
It decreases
How does the lever arm change if you decrease the angle of the force?
It decreases
How does the lever arm change when you decrease the distance to the nut?
It decreases
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
A girl spins around in a circle trying to make herself dizzy. Without changing her position, she starts spinning twice as fast. By how much did her rotational kinetic energy change?
It quadrupled -because rotational kinetic energy is given by the equation Krot = 12Iω2
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
Joe lives on the equator, and Sally lives in Alaska. Which person has the higher speed due to Earth's rotation?
Joe Both Joe and Sally have the same rotational velocity. Joe is going faster than Sally because the equator is further from the axis of rotation than Alaska
Joe lives on the equator, and Sally lives in Alaska. Which person has the higher angular velocity due to Earth's rotation?
Joe and Sally have the same angular velocity Even though Joe is moving more quickly than Sally, they both have the same angular velocity because they both complete one revolution every 24 hours
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
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
Calculate the torque produced by a 40-N force when a pipe extends the length of the wrench to 0.60 m
T= 24 Nm Torque = Lever Arm × Force
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
Inertia depends on mass; rotational inertia depends on mass and something else. What?
The distribution of mass about the axis of rotation
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
A solid sphere and a hollow sphere (spherical shell) of the same mass and same radius rotate with the same amount of kinetic energy. Which one is rotating faster?
The solid sphere Because the rotational kinetic energy is given by the equation Krot = 12Iω2, the object with the smaller moment of inertia would have to spin faster to obtain the same value for the rotational kinetic energy. The hollow sphere is just like the solid sphere, except that you would take the mass near the axis for the solid sphere and shove it outwards towards the surface. Moving mass further from the axis of rotation makes the moment of inertia for the hollow sphere larger than the solid sphere.]
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
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
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
Consider someone in a rotating space habitat. Rotational motion provides _______.
a support force
The rotational inertia of a pencil is greatest about an axis
about its end, like a pendulum
The famous Leaning Tower of Pisa doesn't topple over because its center of gravity is
above a place of support
Multiple the equation for linear momentum by radial distance r and you have
angular momentum
The center of gravity of a basketball is located _______.
at its geometrical center
A vertically-held sledge hammer is easier to balance when the heavier end is
at the top, away from your hand
Toss a baseball bat into the air and it wobbles about its
center of mass
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
The net force exerted on a car traveling in a circular path at constant speed is
directed toward the center of the curve
When the rotational speed of a rotating system doubles, its angular momentum _______.
doubles
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
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
half as fast
Rotational inertia about the midpoint of an object becomes greater with _______.
increased mass and increased distance to mass concentration
If the rotational speed of a rotating habitat in space increases, the weight experienced by occupants
increases
When a twirling ice skater brings her arms inward, her rotational speed
increases
What are the units of measurement for tangential speed? For rotational speed?
m/s for tangential, RPM for rotational
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
more than the weight of the seesaw
A ball that gains speed as it rolls down a hill experiences a
net force and net torque
When a rock tied to a string is whirled in a horizontal circle, doubling the speed _______.
quadruples the tension in the string
A ring and a disk both at rest roll down a hill together. Which rolls slower?
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
rise
As a huge rotating cloud of particles in space gravitate together forming an increasingly dense ball, it shrinks in size and
rotates faster
Centrifugal forces are an apparent reality to observers in a reference frame that is
rotating
A torque acting on an object tends to produce
rotation
The chef at the infamous Fattening Tower of Pizza tosses a spinning disk of uncooked pizza dough into the air. The disk becomes wider during its flight, while its rotational speed
slows
A ring, a disk, and a solid sphere begin rolling down a hill together. Which reaches the bottom first?
sphere
The rotational inertia of your leg is greater when your leg is
straight
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
For a system in mechanical equilibrium, the resultant
torque must be zero and the force must be zero
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
To rotate a stubborn screw, it is best to use a screwdriver that has a
wide handle
Which tin can will roll down an incline in the shortest time, one filled with water or one filled with ice? (Hint: water 'slides' inside the can.)
with water
