Q: A bicycle wheel starts from rest and accelerates at $$\alpha = 2.00\ \text{rad/s}^2. $$What is its angular velocity after $$3.00\ \text{s}$$?

$$\omega = 6.00\ \text{rad/s}$$

Q: A discus thrower accelerates a discus in a circle of radius $$0.80\ \text{m}$$ with angular acceleration $$\alpha = 50\ \text{rad/s}^2$$ and angular velocity $$\omega = 10\ \text{rad/s}. $$What is the magnitude of the total acceleration?

$$a = 40\sqrt{26}\ \text{m/s}^2$$

Q: A point on a rotating disk has both tangential and radial acceleration. Which formula gives the magnitude of the total acceleration?

$$a = \sqrt{a_{\text{tan}}^2 + a_{\text{rad}}^2}$$

Q: A disk rotates from rest with constant angular acceleration $$\alpha. $$Which equation gives the angular displacement $$\theta$$ after time $$t$$?

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

Q: A rotating object has angular velocity $$\omega$$ and radius $$r. $$What is the radial (centripetal) acceleration?

$$a_{\text{rad}} = \$$omega^2$$ r$$

Question 1

A wind turbine blade rotates with a constant angular velocity of $$\omega = 2.5\ 	ext{rad/s}. If $$the tip of the blade is $$r = 40\ 	ext{m}$$ from the axis, what is the linear speed of the tip?

Accepted Answer

$$v = 100\ 	ext{m/s}$$

Question 2

A gyroscope is spinning with an angular velocity $$\$$omega_0$$ = 10\ 	ext{rad/s}$$ and an angular acceleration $$\alpha = -2\ 	ext{rad/s}^2. $$How long will it take for the gyroscope to come to rest?

Accepted Answer

$$t = 5\ 	ext{s}$$

Question 3

Which of the following best describes the sign convention for angular velocity when a wheel rotates counterclockwise?

Accepted Answer

Angular velocity is positive ($$\omega \u003e 0)$$

Question 4

A bicycle wheel starts from rest and accelerates at $$\alpha = 2.00\ 	ext{rad/s}^2. $$What is its angular velocity after $$3.00\ 	ext{s}$$?

Accepted Answer

$$\omega = 6.00\ 	ext{rad/s}$$

Question 5

A merry-go-round spins at a constant angular velocity. If Sofia is twice as far from the axis as Rasheed, what is Sofia's speed compared to Rasheed's?

Accepted Answer

Twice Rasheed's speed

Question 6

A discus thrower accelerates a discus in a circle of radius $$0.80\ 	ext{m}$$ with angular acceleration $$\alpha = 50\ 	ext{rad/s}^2$$ and angular velocity $$\omega = 10\ 	ext{rad/s}. $$What is the magnitude of the total acceleration?

Accepted Answer

$$a = 40\sqrt{26}\ 	ext{m/s}^2$$

Question 7

If a propeller must not exceed a tip speed of $$300\ 	ext{m/s}$$ and rotates at $$1500\ 	ext{rev/min}$$, what is the maximum radius allowed?

Accepted Answer

$$r = 1.91\ 	ext{m}$$

Question 8

The moment of inertia for a solid sphere of mass $$M$$ and radius $$R$$ about its symmetry axis is:

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 9

Suppose you form a sphere and a cylinder from the same mass $$m$$ and radius $$R. $$Which has the larger moment of inertia about its symmetry axis?

Accepted Answer

Cylinder

Question 10

A rigid body rotates with angular velocity $$\omega$$ and has moment of inertia $$I. $$What is its rotational kinetic energy?

Accepted Answer

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

Question 11

If a bicycle chain connects two sprockets, and the front sprocket has twice as many teeth as the rear, what is the ratio of their angular velocities ($$\omega_A$$ for front, $$\omega_B$$ for rear)?

Accepted Answer

$$\omega_B = 2\omega_A$$

Question 12

A point on a rotating disk has both tangential and radial acceleration. Which formula gives the magnitude of the total acceleration?

Accepted Answer

$$a = \sqrt{a_{	ext{tan}}^2 + a_{	ext{rad}}^2}$$

Question 13

Which equation correctly relates linear velocity $$v$$ and angular velocity $$\omega$$ for a point at radius $$r$$?

Accepted Answer

$$v = r\omega$$

Question 14

A solid cylinder of mass $$M$$ and radius $$R$$ rotates about its symmetry axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2}MR^2$

Question 15

A rotating object has angular acceleration $$\alpha$$ and radius $$r. $$What is the tangential acceleration?

Accepted Answer

$$a_{	ext{tan}} = r\alpha$$

Question 16

A disk rotates from rest with constant angular acceleration $$\alpha. $$Which equation gives the angular displacement $$	heta$$ after time $$t$$?

Accepted Answer

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

Question 17

A rotating object has angular velocity $$\omega$$ and radius $$r. $$What is the radial (centripetal) acceleration?

Accepted Answer

$$a_{	ext{rad}} = \$$omega^2$$ r$$

Question 18

A sculpture consists of three point masses connected by massless rods. If the axis passes through A, which mass contributes most to the moment of inertia?

Accepted Answer

The mass farthest from A

Question 19

Which of the following is true about the moment of inertia for a given mass distribution?

Accepted Answer

It depends on the axis of rotation

Rotational Motion: Concepts, Equations, and Applications

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