Chapter 8 physics rotational motion

A person grips the end of the wrench, 0.5 meters from the bolt, and pushes on the end in the direction of the bolt with a force of 50 N. What is the torque exerted on the bolt?

0 N m. Since the force is in the same direction as the wrench, there is no component of the force perpendicular to the wrench, so the torque is zero

A boy and girl are playing on a teeter totter. The boy is three times as massive as the girl. If the boy is sitting 0.5 meters away from the pivot point, how far away should the girl sit such that the two can sit balanced, horizontally?

1.5m. The torque goes as weight times distance, so the distance of the girl from the pivot point must be three times higher than that of the boy.

A person grips a wrench 0.2 meters away from the bolt and pulls in a direction perpendicular to the wrench with a force of 50N. What is the torque exerted on the bolt?

10 N m . Since the force is perpendicular to the wrench, the torque is given by the torque= forces time distance

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

Three people are standing on a spinning merry go round. Person A is standing near the center, person B is standing halfway between the center and edge, and person C is standing. See the edge. Which person takes the longest amount of time to complete one circle ?

All three complete the circle in the same amount of time. This means that person C is moving the fastest since he covers a larger circumference than the others

What is needed to change a system's angular momentum?

Angular momentum changes with an applied external torque.

If a spinning skater pulls her arms in so as to reduce her rotational inertia by half, by how much will her rate of spin increase?

Angular momentum remains the same, while her rate of spin doubles.

Which More Accurately Describes What Happens in the Circular Spin Cycle of a Washing Machine?

Clothes are forced into a circular path while water is not

Under what condition is the angular momentum of an object conserved?

If there is no net torque acting on it.

The Rotational Inertia of an Object Is Greater When Most of the Mass Is Located

away from the rotational axis.

center of mass

is the average position of all the mass that makes up the object

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

why does a circus tightrope walker carry a long pole?

to aid in balance. Much of the mass of the pole is far from the axis of rotation, its midpoint. The pole, therefore, has considerable rotational inertia. longer pole=Better!

A condition for mechanical equilibrium is that the sum of the forces acting equal zero. Another condition is that the sum of the

torques equal zero

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

Tangential (linear) speed ~ radial distance × rotational speed

v ~ rω

How do linear momentum and angular momentum differ?

Angular momentum depends on the distribution of mass, whereas linear momentum depends on the total mass.

Rank them in reaching the bottom: winner, second place, and third place. for the rings

B,A,C

Why it is easier to remove an old bolt if we add an extension to the wrench handle?

Because a higher torque is applied

Rate the rotational inertias about each axis from large to small. for the pencils

C, B, A

When we studied the concept of work, we learned that work = force x distance. Now we learn that torque = force x distance. What's different about these two definitions?

For work, distance and force are in the same direction; for torque they are perpendicular to each other.

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.

conversation of angular momentum

If no external net torque acts on a rotating system, the angular momentum of that system remains constant

An ice skater is spinning while holding her arms out perpendicular to her body. As she brings her arms towards her body, the rotational speed

Increases. Due to angular momentum being conserved, the rotational speed needs to increase if the moment of inertia decreases

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.

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

If you toss a stick into the air, it appears to wobble all over the place. Specifically, about what place?

It will rotate about the center of mass.

Angular momentum = rotational inertia × rotational velocity . Angular momentum is a conserved quantity... Therefore, the product of I and ω has to be constant.

L = Iω p = mv

Where is the center of mass of Earth's crust?

Like a giant basketball, Earth's crust is a spherical shell with its center of mass at Earth's center.

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

Can an object have more than one CG?

No. A rigid object has one CG. If an object is nonrigid, such as a piece of clay or putty, and is distorted into different shapes, then its CG may change as its shape changes. Even then, it has one CG for any given shape.

How is rotational inertia similar to inertia as studied in previous chapters?

Rotational inertia is the resistance to a change in rotational motion, which is similar to inertia which is a resistance to a change in velocity.

A record player is spinning with a certain rotational speed. One ant is standing half way between the center of the record and the edge, and another ant is standing on the edge. Which ant is moving faster?

The ant in the edge. Since the ant on the edge travels around a bigger circle in the same amount of time as the other ant, it is moving faster

Where is its center of mass for a baseball bat--closer to the grip or the thick end?

The center of mass is closer to the thick end.

On what does the angular momentum of an object depend?

The rate at which that the object rotates. The axis of rotation. The shape of the object .The mass of the object

For a rotating object experiencing no net external torque, what happens to the rate of rotation if the moment of inertia of the object decreases by a factor of 2?

The rate of rotation increases by a factor of 2. L = Iω

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 Dr. Hewitt cuts the broom right through the center of gravity, how do the weights of the two sides of the broom compare?

The shorter side, where the bristles of the broom are, has a greater weight than the handle.

A record player is spinning with a certain rotational speed. An ant is standing somewhere on the record without slipping. Suddenly, the rotational speed of the record player is doubled (it is spinning twice as quickly). What happens to ants tangential speed?

The tangential speed doubles. The ant travels around the same circle in half the time it used to take, so the tangential speed is twice as high.

How does the tapered rim of a wheel on a railroad train rolling along a track allow one part of the rim to roll faster than another part?

The tangential speed is proportional to the radius. The inside of the wheel rolls on a larger radius than the outside of the wheel.

Explain why a long pole is more beneficial to a tightrope walker if the pole droops.

The tendency of the pole to resist rotation aids the acrobat.

How does the torque due to the weight of one side of the broom exerted around the balance point compare with the torque exerted by the weight of the other side of the broom around the balance point?

The torque due to the weight of the shorter side (the bristles of the broom) is equal in magnitude to the torque due to the weight of the longer side, and opposite in direction.

Is it an inward force or an outward force that is exerted on the clothes during the spin cycle of a washing machine?

The tub of the machine exerts centripetal inward force on clothes.

When you whirl a can overhead by a string in a circular path, what is the direction of the force exerted on the can?

Toward the center of the circle.

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.

Without the small rotor on its tail, the helicopter and the main rotor would rotate in opposite directions. The small rotor provides a torque to offset the rotational motion that the helicopter would otherwise have.

The center of gravity of a basketball is located

at its geometrical center

Where is the center of gravity of the broom that Dr. Hewitt holds up?

at the balance point

An object or system of objects will maintain its angular momentum unless acted upon

by an external net torque

Zero-angular-momentum

by turning one part of the body against the other

The greater the rotational inertia of an object, the greater the difficulty in

changing its rotational state

you can touch your toes if your center of gravity is above your base of support but if you stand against a wall, you cant...

counterbalance and center of gravity protrudes beyond your feet

Suppose you double the speed at which you round a curve. By what factor must the centripetal force change to prevent you from skidding?

double

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 v ~ rω

When Two Children of Different Weights Balance on a Seesaw, They Each Produce

equal-magnitude torques in opposite directions.

If we draw a line straight down from the center of gravity of an object of any shape and it falls inside the base of the object, then the object is in stable

equilibrium

When a Car Is Braked to a Stop, Unless It Is a Hybrid or Electric Car, Its Kinetic Energy Is Transformed To

heat

Rotational inertia of an object rotating about an axis becomes greater with

increased mass and increased distance to mass concentration

an object rotating about an axis tends to remain rotating about the same axis unless

interfered with by some external influence(the external influence is torque)

The rotational speed of every point of a rotating rigid object

is the same

Short legs have ____ rotational inertia than long legs

less

To improve the performance of a racing bicycle, the mass of the tires and rims is reduced so there is

less rotational inertia

torques equal

level arm x force

Anything that is in mechanical equilibrium doesn't accelerate

linearly or rotationally

Like inertia for linear motion, rotational inertia depends on

mass (distributed around axis of rotation)

centripetal force equation

mass x tangential speed^2/radius

A Torque Is a Force

multiplied by a lever arm

A ruler is in equilibrium on the tip of your finger only if

net torque and net force are zero

james finds it difficult to muster enough torque to turn the stubborn bolt with the wrench. he wishes he had a pipe handy to effectively lengthen the wrench handle, but doesn't. he does, however, have a piece of rope. will torque be increased if he pulls as hard on he rope as shown?

no the torque will be the same because the lever-arm distance is the same in both cases

Bodies that are rotating tend to remain rotating, while

nonrotating bodies tend to remain nonrotating

When a rock tied to a string is whirled in a horizontal circle, doubling the speed

quadruples the tension in the string

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

torque causes

rotation

the broom balances at its center of gravity if you saw the broom into two parts through the center of gravity and then weigh each part on a scale. which part will weigh more?

short broom part.

angular momentum

the "inertia of rotation" of rotating objects. rotational inertia x rotational velocity

The greater the distance between an object's mass concentration and the axis the...

the greater the rotational inertia

center of gravity

the point around which an object's weight is evenly distributed.

The angular momentum of our solar system nicely remains the same century after century. What would be needed for it to be altered?

A force external to our solar system would be the culprit. No force internal to the solar system could do it!

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.

Inertia depends on mass. Does rotational inertia depend on mass also?

Rotational inertia depends on the distribution of mass about the axis of rotation.

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.

The moment of inertia of a rotating ice skater is largest when

The arms are held perpendicular to her body. The moment of inertia of something is larger when more mass is further from the axis of rotation

What kind of force acts on a ladybug inside a can that is whirled in a circular path?

The can exerts on the ladybug an inward centripetal force.

How does the angular momentum of a cat change in falling from a tree?

The cat rotates its body through an angle, but the angular momentum of the cat remains constant.

Do seat belts provide a centripetal or centrifugal force on a passenger in a car rounding a curve?

The seat belts provide a centripetal force on the passenger.

How do clockwise and counterclockwise torques compare when a system is balanced?

They are equal in magnitude and opposite in direction.

If a pipe effectively extends a wrench handle to three times its length, by how much will the torque increase for the same applied force?

Three times more leverage for the same force produces three times more torque.

What kind of motion does a torque tend to impart to an object?

Torque tends to twist or change the state of rotation of the object

A tapered cup rolled on a flat surface makes a circular path.Does this mean the tangential speed of the wide-end rim differs with that of the narrow-end rim?

Yes, the tangential speed of the wide end is faster.

Because of rotational inertia, a solid cylinder starting from rest will roll down an incline faster than

a hoop. a hoop has greater rotational inertia and is harder to start rolling

The tangential speed on the outer edge of a rotating carousel is

greater than toward the center

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.

For Round Objects Rolling Down an Incline, the Fastest Objects Are Generally Those With The

lowest rotational inertia compared with mass.​

What are the units of measurement for tangential speed and rotational speed?

m/s for tangential, rpm for rotational

Is your support base larger, smaller, or the same when you stand with your feet wide apart?

larger

Balancing an object provides a simple method of

locating its center of gravity

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