Q: A standard turntable rotates at a constant angular speed of $$33 \frac{1}{3}$$ rpm. What is the angular velocity $$\omega in $$radians per second?

$$\omega = 3.49 \, \text{rad/s}$$

Q: A person is holding an $$8.0 \, \text{kg}$$ weight at arm's length, a distance of $$0.55 \, \text{m}$$ from her shoulder joint. What is the magnitude of the torque about the shoulder due to the weight?

$$43 \, \text{N} \cdot \text{m}$$

Q: A $$0.50 \, \text{kg}$$ mass is attached to a $$0.20 \, \text{m}$$ string and swung in a horizontal circle at $$2.0 \, \text{m/s}. $$What is the magnitude of the angular momentum of the mass?

$$0.40 \, \text{kg} \cdot \text{m}^2/\text{s}$$

Question 1

A standard turntable rotates at a constant angular speed of $$33 \frac{1}{3}$$ rpm. What is the angular velocity $$\omega in $$radians per second?

Accepted Answer

$$\omega = 3.49 \, 	ext{rad/s}$$

Question 2

A pulley has an initial angular speed of $$12.5 \, 	ext{rad/s}$$ and a constant angular acceleration of $$-4.00 \, 	ext{rad/s}^2. $$Through what angle does the pulley turn before coming to rest?

Accepted Answer

$$39.1 \, 	ext{rad}$$

Question 3

An athlete runs around a circular track of radius $$R at a $$constant speed $$v. $$What is the magnitude of the angular acceleration of the athlete?

Accepted Answer

$$0$$

Question 4

A person is holding an $$8.0 \, 	ext{kg}$$ weight at arm's length, a distance of $$0.55 \, 	ext{m}$$ from her shoulder joint. What is the magnitude of the torque about the shoulder due to the weight?

Accepted Answer

$$43 \, 	ext{N} \cdot 	ext{m}$$

Question 5

A force $$F is $$applied to a solid disk of mass $$8.0 \, 	ext{kg}$$ and radius $$0.50 \, 	ext{m}$$, causing it to rotate about its center. If the disk accelerates at $$3.0 \, 	ext{rad/s}^2$$, what is the magnitude of the force $$F$$ applied at the rim?

Accepted Answer

$$12.0 \, 	ext{N}$$

Question 6

A uniform rod of length $$L$$ and mass $$M is $$pivoted at one end and released from rest in a horizontal position. What is the angular speed $$\omega of $$the rod as it passes through the vertical position?

Accepted Answer

$$\omega = \sqrt{\frac{3g}{L}}$$

Question 7

A $$2.0 \, 	ext{kg}$$ mass is attached to a light string that is wrapped around a solid disk of radius $$0.20 \, 	ext{m}$$ and mass $$1.0 \, 	ext{kg}. If $$the mass is released from rest and falls $$1.5 \, 	ext{m}$$, what is its speed just before hitting the floor? (Assume no friction.)

Accepted Answer

$$2.7 \, 	ext{m/s}$$

Question 8

Two masses, $$m_1$$ and $$m_2$$, are connected by a light string and hang vertically next to each other, each mass is under gravity. If $$m_1 = 2.0$$ \, 	ext{kg}$$ and m_2$ = 3.0 \, 	ext{kg}$$, what is the tension in the string between them?

Accepted Answer

$$T = 19.6 \, 	ext{N}$$

Question 9

A solid sphere and a solid disk, each of mass $$M$$ and radius $$R$$, are released from rest at the top of an incline of height $$h. $$Which object reaches the bottom first, and why?

Accepted Answer

The sphere, because it has a smaller moment of inertia relative to its mass.

Question 10

A torque of $$12 \, 	ext{N} \cdot 	ext{m} is $$applied to a solid, uniform disk of radius $$0.50 \, 	ext{m}. If $$the disk accelerates at $$3.0 \, 	ext{rad/s}^2$$, what is the mass of the disk?

Accepted Answer

$$6.4 \, 	ext{kg}$$

Question 11

A satellite orbits a planet in a circular orbit of radius $$r. A $$second satellite passes through the same orbit but at twice the speed. By what factor is the magnitude of the angular momentum $$L of $$the second satellite different from the first?

Accepted Answer

It is four times as large.

Question 12

A $$2.0 \, 	ext{kg}$$ block is attached to a light string that is wrapped around a pulley of radius $$0.10 \, 	ext{m}$$ and mass $$0.50 \, 	ext{kg}. If $$the block is released from rest and falls $$1.0 \, 	ext{m}$$, what is its speed just before hitting the floor? (Assume no friction.)

Accepted Answer

$$2.6 \, 	ext{m/s}$$

Question 13

A figure skater spins with arms extended and then pulls her arms in close to her body. What happens to her angular velocity and why?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases.

Question 14

A uniform rod of length $$L$$ and mass $$M is $$pivoted at its center. What is its moment of inertia about the pivot?

Accepted Answer

$$I = \frac{1}{12}ML^2$

Question 15

A $$0.50 \, 	ext{kg}$$ mass is attached to a $$0.20 \, 	ext{m}$$ string and swung in a horizontal circle at $$2.0 \, 	ext{m/s}. $$What is the magnitude of the angular momentum of the mass?

Accepted Answer

$$0.40 \, 	ext{kg} \cdot 	ext{m}^2/	ext{s}$$

Question 16

A car has a flat tire. The driver finds that upon reapplying force at a point where the lever arm is twice as long, the torque produced is:

Accepted Answer

Twice as large as before.

Physics Exam: Rotational Motion, Forces, and Energy Study Notes

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