Q: A disk rotates with constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$, what is its angular displacement $$\theta$$ after time t$?

$$\theta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Question 1

A Ferris wheel rotates at a constant angular velocity. If the radius of the wheel is doubled but the angular velocity remains the same, what happens to the linear velocity of a point on the rim?

Accepted Answer

It is doubled.

Question 2

Which equation correctly relates the angular displacement $$	heta to $$the arc length $$\ell$$ and radius $$r of a $$circle?

Accepted Answer

$$	heta = \ell / r$$

Question 3

A wheel starts from rest and accelerates at a constant angular acceleration $$\alpha. $$Which equation gives the angular velocity $$\omega$$ after time $$t$$?

Accepted Answer

$$\omega = \$$omega_0$$ + \alpha t$$

Question 4

A solid cylinder and a hollow cylinder of equal mass and radius roll down an incline without slipping. Which reaches the bottom first and why?

Accepted Answer

The solid cylinder, because it has less rotational inertia.

Question 5

Which of the following best describes torque?

Accepted Answer

Torque is the product of force and the perpendicular distance from the axis of rotation.

Question 6

A person uses a wrench to loosen a bolt. Which action increases the torque applied to the bolt?

Accepted Answer

Using a longer wrench.

Question 7

If the net torque on a system is zero, what can be said about its angular momentum?

Accepted Answer

It remains constant.

Question 8

A rotating disk has a rotational inertia $$I$$ and angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} I \$$omega^2$$

Question 9

A gymnast pulls her arms in while spinning, reducing her rotational inertia. What happens to her angular velocity, assuming no external torque acts?

Accepted Answer

It increases.

Question 10

Which formula gives the angular momentum $$L of a $$rotating object?

Accepted Answer

$$L = I \omega$$

Question 11

A wheel of radius $$r$$ rolls without slipping at speed $$v. $$What is its angular speed $$\omega$$?

Accepted Answer

$$\omega = v / r$$

Question 12

A rotating object has both translational and rotational kinetic energy. Which equation gives its total kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} M v_{CM}^2 + \frac{1}{2} I_{CM} \$$omega^2$$

Question 13

A force $$F is $$applied at a distance $$r$$ from the axis of rotation at an angle $$	heta to $$the lever arm. What is the torque $$	au$$ produced?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 14

Which of the following statements about rotational inertia is correct?

Accepted Answer

Rotational inertia depends on both mass and how mass is distributed relative to the axis of rotation.

Question 15

A disk rotates with constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$, what is its angular displacement $$	heta$$ after time t$?

Accepted Answer

$$	heta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Question 16

A child spins a merry-go-round by applying a force at its edge. Which of the following will increase the angular acceleration of the merry-go-round?

Accepted Answer

Increasing the applied force.

Question 17

Which of the following is true about the period $$T$$ and frequency $$f of a $$rotating object?

Accepted Answer

$$T = 1 / f$$

Question 18

A torque $$	au$$ does work $$W as it $$rotates an object through an angle $$\Delta 	heta. $$What is the work done?

Accepted Answer

$$W = 	au \Delta 	heta$$

Question 19

A bicycle wheel rotates at $$10$$ rad/s. What is the frequency of rotation in Hz?

Accepted Answer

$$f = 10 / (2 \pi)$$

Rotational Motion: Principles, Quantities, and Dynamics

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