The fan blade is speeding up. What are the signs of ω and α? [Please use the historical convention in which we define positive angular displacement to be counter-clockwise.]

1. ω is positive and α is positive.
2. ω is positive and α is negative.
3. ω is negative and α is positive.
4. ω is negative and α is negative.

Question 10.1

The fan blade is slowing down. What are the signs of ω and α? [Please use the historical convention in which we define positive angular displacement to be counter-clockwise.]

1. ω is positive and α is positive.
2. ω is positive and α is negative.
3. ω is negative and α is positive.
4. ω is negative and α is negative.

Question 10.2

Which dumbbell has the larger rotational inertia about the midpoint of the rod? The connecting rod is massless.

1. Dumbbell A
2. Dumbbell B
3. Their rotational inertias are the same.

Question 10.3

• Mass m₂ is on a frictionless table. It is attached to a cord that wraps around a massive pulley of radius R, and is attached to a hanging mass m₁. Assume the axle of the pulley can rotate without friction.
• After the system is released, how does the magnitude of the tension in the rope attached to m₁ compare to the weight of m₁, m₁ g?
• T₁ > m₁g
• T₁ < m₁g
• T₁ = m₁g
• T₁ and m₁g cannot be compared

I_pulley

Question 10.4

• Mass m₂ is on a frictionless table. It is attached to a cord that wraps around a massive pulley of radius R, and is attached to a hanging mass m₁. Assume the axle of the pulley can rotate without friction.
• After the system is released, how do the tensions in the two ropes compare?
• T₁ > T₂
• T₁ < T₂
• T₁ = T₂
• T₁ and T₂ cannot be compared

​

I_pulley

Question 10.5

• Mass m₂ is on a frictionless table. It is attached to a cord that wraps around a massive pulley of radius R, and is attached to a hanging mass m₁. Assume the axle of the pulley can rotate without friction.
• After the system is released, what is the net torque on the pulley [define counter-clockwise = positive]?
• T₁ R − T₂R
• T₂ R − T₁R
• T₁ R + T₂R
• T₁ R

I_pulley

Question 10.6

Which description below best describes the Moment of Inertia, often given the symbol I, and measured in units of kg m²?

1. the rotational analog of kinetic energy.
2. the rotational analog of mass.
3. the rotational analog of momentum.
4. the pivot point in a static equilibrium problem.
5. the tendency for anything that is rotating to continue rotating.

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Question 10.7

Cross Product Practice

Question 10.8

Question 10.9

Cross Product Practice

Question 10.10

Cross Product Practice

Magnitude:

Question 10.11

Question 10.12

A figure skater stands on one spot on the ice (assumed frictionless) and spins around with her arms extended.

When she pulls in her arms, she reduces her rotational inertia and her angular speed increases in order to conserve rotational momentum .

Compared to her initial rotational kinetic energy, her rotational kinetic energy after she has pulled in her arms is

1. Larger
2. Smaller
3. The same

• A car is driving East on Bloor Street.
• What is the direction of the angular momentum vector of one of the wheels of this car?
• North
• East
• South
• West
• up
• down

Question 10.13

Question 10.14

• A solid disk is released from rest and rolls without slipping down an incline. A frictionless block of ice is released from rest and slides down a frictionless incline of the same angle. Which reaches the bottom first?
• A: disk wins
• B: block of ice wins
• C: tie

​

VS.

Question 10.15

• A solid disk is released from rest and rolls without slipping down an incline. A metal hoop of the same mass is released from rest and rolls without slipping down an incline of the same angle. Which reaches the bottom first?
• A: solid disk wins
• B: hoop wins
• C: tie

​

VS.

• Two soup cans begin at the top of an incline, are released from rest, and allowed to roll without slipping down to the bottom. Which will win?

Predict:

1. Cream of Mushroom will win
2. Chicken Broth will win
3. Both will reach the bottom at about the same time.

Question 10.16