AP Physics 1 Review Chs 8&9Rotational Kinematics and Dynamics

· Be able to perform calculations with the rotational kinematics equations and understand the

relationship between rotational and translational quantities· Understand the factors that affect torque and be able to calculate torque ()· Understand the concept of center of gravity and know that the torque produced by an object’s

weight acts from the center of gravity· Be able to solve static equilibrium problems such as a balanced meter stick with hanging masses,

ladder leaning against wall, beams supported by cables, etc. · Understand translational and rotational equilibrium and be able to identify each· Understand the concept of moment of inertia· Understand that a net torque is required for angular acceleration and be able to use in calculations· Understand rotational kinetic energy and be able to use in calculations· Be able to calculate changes in mechanical energy for an object rolling without slipping up or

down an incline; understand what would happen if the incline were frictionless· Understand conservation of angular momentum and be able to use in calculations · Understand what happens with angular momentum, angular speed, moment of inertia, and

rotational kinetic energy as a skater moves her arms inward or outward

Bonnie and Klyde I

w

BonnieKlyde

Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every2 seconds.

Klyde’s angular velocity is:

a) same as Bonnie’s

b) twice Bonnie’s

c) half of Bonnie’s

d) one-quarter of Bonnie’s

e) four times Bonnie’s

The angular velocity w of any point

on a solid object rotating about a

fixed axis is the same. Both Bonnie

and Klyde go around one revolution

(2p radians) every 2 seconds.

Bonnie and Klyde I

w

BonnieKlyde

Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every2 seconds.

Klyde’s angular velocity is:

a) same as Bonnie’s

b) twice Bonnie’s

c) half of Bonnie’s

d) one-quarter of Bonnie’s

e) four times Bonnie’s

Bonnie and Klyde II

w

BonnieKlyde

a) Klyde

b) Bonnie

c) both the same

d) linear velocity is zero for both of them

Bonnie sits on the outer rim of amerry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity?

Their linear speeds v will be

different because v = r w and

Bonnie is located farther out

(larger radius r) than Klyde.

w

Bonnie

Klyde

BonnieKlyde V21

V

Bonnie and Klyde II

Follow-up: Who has the larger centripetal acceleration?

a) Klyde

b) Bonnie

c) both the same

d) linear velocity is zero for both of them

Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity?

Suppose that the speedometer of a truck is set to read the linear speed of the truck but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck?

a) speedometer reads a higher speed than the true

linear speed

b) speedometer reads a lower speed than the true linear speed

c) speedometer still reads the true linear speed

Truck Speedometer

Suppose that the speedometer of a truck is set to read the linear speed of the truck but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck?

a) speedometer reads a higher speed than the true

linear speed

b) speedometer reads a lower speed than the true linear speed

c) speedometer still reads the true linear speed

The linear speed is v = wR. So when the speedometer measures

the same angular speed w as before, the linear speed v is actually

higher, because the tire radius is larger than before.

Truck Speedometer

Using a Wrench

You are using a wrench to

loosen a rusty nut. Which

arrangement will be the

most effective in loosening

the nut?

a

cd

b

e) all are equally effective

You are using a wrench to

loosen a rusty nut. Which

arrangement will be the

most effective in loosening

the nut?

a

cd

b

Because the forces are all the same, the only difference is the lever arm. The arrangement with the largest lever arm (case #2) will

provide the largest torque.

e) all are equally effective

Follow-up: What is the difference between arrangement 1 and 4?

Using a Wrench

Two forces produce the same

torque. Does it follow that they

have the same magnitude?

a) yes

b) no

c) depends

Two Forces

Two forces produce the same

torque. Does it follow that they

have the same magnitude?

a) yes

b) no

c) depends

Because torque is the product of force times distance, two different

forces that act at different distances could still give the same torque.

Two Forces

Follow-up: If two torques are identical, does that mean their forces are identical as well?

Closing a Door

In which of the cases shown below

is the torque provided by the

applied force about the rotation

axis biggest? For all cases the

magnitude of the applied force is

the same.

a) F1

b) F3

c) F4

d) all of them

e) none of them

Closing a Door

a) F1

b) F3

c) F4

d) all of them

e) none of them

In which of the cases shown below

is the torque provided by the

applied force about the rotation

axis biggest? For all cases the

magnitude of the applied force is

the same.

The torque is t = rFsin, and

so the force that is at 90° to the

lever arm is the one that will have

the largest torque. Clearly, to

close the door, you want to push

perpendicularly!!

When a tape is played on a cassette deck, there is a tension in the tape that applies a torque to the supply reel. Assuming the tension remains constant during playback, how does this applied torque vary as the supply reel becomes empty?

a) torque increases

b) torque decreases

c) torque remains constant

Cassette Player

When a tape is played on a cassette deck, there is a tension in the tape that applies a torque to the supply reel. Assuming the tension remains constant during playback, how does this applied torque vary as the supply reel becomes empty?

a) torque increases

b) torque decreases

c) torque remains constant

As the supply reel empties, the lever arm decreases because the radius of the reel (with tape on it) is decreasing. Thus, as the playback continues, the applied torque diminishes.

Cassette Player

Moment of Inertia

a) solid aluminum

b) hollow gold

c) same

same mass & radius

solid hollow

Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold.

Which one has the bigger moment of inertia about an axis through its center?

Moment of Inertia

same mass & radius

solid hollow

Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold.

Which one has the bigger moment of inertia about an axis through its center?

Moment of inertia depends on mass and distance from axis squared. It is bigger for the shell because its mass is located farther from the center.

a) solid aluminum

b) hollow gold

c) same

Figure Skater

a) the same

b) larger because she’s rotating faster

c) smaller because her rotational

inertia is smaller

A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be

Figure Skater

a) the same

b) larger because she’s rotating faster

c) smaller because her rotational inertia is smaller

A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertiaand spins faster so that her angular momentum is conserved. Comparedto her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be:

KErot = I 2 = L (used L = I ).

Because L is conserved, larger means larger KErot. The “extra”

energy comes from the work she

does on her arms.

12

12

Two Disks

a) disk 1

b) disk 2

c) not enough info

Two different spinning disks have the same angular momentum, but disk 1 has more kinetic energy than disk 2.

Which one has the bigger moment of inertia?

LL

Disk 1Disk 2

Two Disks

Two different spinning disks have the same angular momentum, but disk 1 has more kinetic energy than disk 2.

Which one has the bigger moment of inertia?

a) disk 1

b) disk 2

c) not enough info

LL

Disk 1Disk 2

KE = I 2 = L2 (2 I) (used L = I ).

Because L is the same, bigger I means smaller KE.

12 /

Balancing Rod

1kg

1m

A 1-kg ball is hung at the end of a rod

1-m long. If the system balances at a

point on the rod 0.25 m from the end

holding the mass, what is the mass of

the rod?

a) ¼ kg

b) ½ kg

c) 1 kg

d) 2 kg

e) 4 kg

1 kg

X

CM of rod

same distance mROD = 1 kg

A 1-kg ball is hung at the end of a rod

1-m long. If the system balances at a

point on the rod 0.25 m from the end

holding the mass, what is the mass of

the rod?

The total torque about the pivot

must be zero !! The CM of the

rod is at its center, 0.25 m to the

right of the pivot. Because this

must balance the ball, which is

the same distance to the left of

the pivot, the masses must be

the same !!

a) ¼ kg

b) ½ kg

c) 1 kg

d) 2 kg

e) 4 kg

Balancing Rod

Tipping Over I

1 2 3

a) all

b) 1 only

c) 2 only

d) 3 only

e) 2 and 3

A box is placed on a ramp in the

configurations shown below. Friction

prevents it from sliding. The center of

mass of the box is indicated by a red dot

in each case. In which case(s) does the

box tip over?

Tipping Over I

1 2 3

a) all

b) 1 only

c) 2 only

d) 3 only

e) 2 and 3

A box is placed on a ramp in the

configurations shown below. Friction

prevents it from sliding. The center of

mass of the box is indicated by a red dot

in each case. In which case(s) does the

box tip over?

The torque due to gravity acts

like all the mass of an object is

concentrated at the CM.

Consider the bottom right corner

of the box to be a pivot point.

Tipping Over II

a) case 1 will tip

b) case 2 will tip

c) both will tip

d) neither will tip

Consider the two configurations of

books shown below. Which of the

following is true?

1/2

1/4 1/2

1/4

1 2

Tipping Over II

The CM of the system is

midway between the CM of

each book. Therefore, the

CM of case #1 is not over the

table, so it will tip.

a) case 1 will tip

b) case 2 will tip

c) both will tip

d) neither will tip

Consider the two configurations of

books shown below. Which of the

following is true?

1/2

1/4 1/2

1/4

1 2