Q: A wheel of mass $$M$$ and radius $$R$$ rolls without slipping with angular velocity $$\omega. $$What is the total kinetic energy of the wheel?

$$\frac{1}{2} I \$$omega^2$$ + \frac{1}{2} M v_{\text{cm}}^2$$

Question 1

A wrench is used to loosen a bolt. A force $$F is $$applied at a distance $$R$$ from the bolt, making an angle $$	heta$$ with the wrench. Which of the following correctly expresses the magnitude of the torque $$	au$$ produced by this force?

Accepted Answer

$$	au = RF \sin 	heta$$

Question 2

A solid sphere and a hollow spherical shell have the same mass $$M$$ and radius $$R. $$Which one has the greater moment of inertia about an axis through its center?

Accepted Answer

The hollow spherical shell

Question 3

A wheel of mass $$M$$ and radius $$R$$ rolls without slipping with angular velocity $$\omega. $$What is the total kinetic energy of the wheel?

Accepted Answer

$$\frac{1}{2} I \$$omega^2$$ + \frac{1}{2} M v_{	ext{cm}}^2$$

Question 4

A figure skater spins with arms outstretched and then pulls her arms in close to her body. Which of the following statements is correct, assuming negligible friction?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases

Question 5

A child of mass $$25\ \mathrm{kg}$$ sits at the center of a merry-go-round of radius $$2\ \mathrm{m}$$ and moment of inertia $$500\ \mathrm{kg\cdot m^2$}$$, rotating at $$\$$omega_1$$ = \frac{2\pi}{5}\ \mathrm{rad/s}. $$The child then moves to the rim. What is the new angular speed $$\$$omega_2$$ of the system?

Accepted Answer

$$\$$omega_2$$ = \frac{500}{600} \$$omega_1$$

Question 6

Two disks are mounted on the same axle. Disk 1 (moment of inertia $$I_1) $$rotates with angular velocity $$\$$omega_1$$, and disk 2 (moment of inertia I_2$) is at rest. If disk 2 is dropped onto disk 1 and they rotate together, what is their final angular velocity $$\omega_f$$?

Accepted Answer

$$\omega_f = \frac{I_1$}{I_1$ + I_2$} \$$omega_1$$

Question 7

A person stands on a frictionless rotating platform at rest. She begins walking clockwise along the edge. What happens to the platform?

Accepted Answer

It rotates counterclockwise to conserve angular momentum

Question 8

Which of the following is NOT a condition for static equilibrium of a rigid body?

Accepted Answer

The net acceleration of the center of mass must be nonzero

Question 9

A ladder leans against a frictionless wall and rests on a rough floor. Which force is responsible for preventing the ladder from sliding away from the wall?

Accepted Answer

The friction force at the floor

Question 10

If a force passes through the axis of rotation (i.e., $$R = 0$$), what is the torque produced by this force about that axis?

Accepted Answer

Zero

Question 11

A uniform beam is supported at both ends and a heavy object is placed at its center. Where does the gravitational force act for the purpose of calculating torque?

Accepted Answer

At the center of mass of the beam plus the position of the object

Question 12

A dancer balances on one foot. For her to remain in static equilibrium, which statement must be true?

Accepted Answer

The line of action of her weight must pass through her supporting foot

Question 13

Which of the following best describes the right-hand rule for determining the direction of angular momentum?

Accepted Answer

Curl the fingers of your right hand in the direction of rotation; your thumb points in the direction of angular momentum

Question 14

A force $$F is $$applied at a distance $$R$$ from a pivot at an angle $$	heta = 0^\circ to $$the position vector. What is the torque about the pivot?

Accepted Answer

$$0$$

Question 15

A uniform rod of length $$L$$ and mass $$M is $$pivoted at one end and held horizontally. What is the magnitude of the torque due to gravity about the pivot?

Accepted Answer

$$\frac{1}{2} M g L$$

Question 16

A disk rotates counterclockwise. According to the right-hand rule, what is the direction of its angular velocity vector?

Accepted Answer

Upward along the axis of rotation

Question 17

Which of the following statements about the analogy between linear and rotational dynamics is correct?

Accepted Answer

Force corresponds to torque, mass to moment of inertia, and acceleration to angular acceleration

Question 18

A uniform ladder leans against a wall at an angle $$	heta. If $$the ladder is in static equilibrium, which of the following must be true?

Accepted Answer

The sum of all torques about any point is zero

Rotational Motion, Angular Momentum, and Static Equilibrium

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