Q: If a rotating object has a constant angular acceleration $$\alpha$$, which equation gives the angular displacement $$\theta$$ after time $$t if it $$starts from rest?

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

Question 1

A washing machine drum has an internal diameter of $$0.470\ \mathrm{m}$$ and spins at $$640\ \mathrm{rev/min}. $$What is the maximum tangential speed of the laundry in the drum?

Accepted Answer

$$v = 31.5\ \mathrm{m/s}$$

Question 2

Convert an angular displacement of $$180^\circ to $$radians.

Accepted Answer

$$\pi\ \mathrm{rad}$$

Question 3

Which equation correctly relates the linear speed $$v to $$the angular velocity $$\omega$$ and radius $$r$$ for a point on a rotating object?

Accepted Answer

$$v = r\omega$$

Question 4

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

Accepted Answer

The solid sphere, because it has a smaller moment of inertia.

Question 5

What is the moment of inertia $$I$$ for a thin rod of mass $$M$$ and length $$L$$ rotating about its center?

Accepted Answer

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

Question 6

A yo-yo is modeled as a solid disk of mass $$M$$ and radius $$R. If it $$drops a distance $$h$$ while unwinding, what is the speed $$v_{cm} of $$its center of mass?

Accepted Answer

$$v_{cm} = \sqrt{\frac{4gh}{3}}$$

Question 7

Which of the following best describes the total kinetic energy of a rolling object (without slipping)?

Accepted Answer

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

Question 8

A uniform marble rolls down a symmetric bowl from height $$h. If $$the bowl is frictionless, how high will the marble rise on the opposite side?

Accepted Answer

$$h$$

Question 9

If a rotating object has a constant angular acceleration $$\alpha$$, which equation gives the angular displacement $$	heta$$ after time $$t if it $$starts from rest?

Accepted Answer

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

Question 10

A wheel rotates counterclockwise with increasing speed. What are the signs of its angular velocity $$\omega$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$\omega \u003e 0$$, $$\alpha \u003e 0$$

Question 11

What is the ratio of the maximum radial force on laundry in a washing machine at $$640\ \mathrm{rev/min} to $$that at $$423\ \mathrm{rev/min}$$, assuming the radius is constant?

Accepted Answer

$$\left(\frac{640}{423}\$$right)^2$$

Question 12

Which of the following is the correct expression for the radial (centripetal) acceleration $$a_{rad} of a $$point at distance $$r$$ from the axis, rotating with angular velocity $$\omega$$?

Accepted Answer

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

Question 13

A rotating rigid body has mass $$m$$ and is moving. Which form of energy must it possess?

Accepted Answer

Kinetic energy

Question 14

If a wheel rotates $$90^\circ$$, what is the angular displacement in radians?

Accepted Answer

$$\frac{\pi}{2}\ \mathrm{rad}$$

Question 15

Which of the following is the correct formula for the moment of inertia $$I of a $$system of particles?

Accepted Answer

$$I = \sum m_ir_i^2$

Question 16

A disk rotates with constant angular acceleration. If its initial angular velocity is zero, which equation gives its angular velocity $$\omega$$ after time $$t$$?

Accepted Answer

$$\omega = \alpha t$$

Rotational Motion: Angular Quantities, Kinematics, and Energy

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