Q: Which equation correctly gives the angular displacement $$\theta$$ for a body with constant angular acceleration $$\alpha_z$$ and initial angular velocity $$\omega_{0z}$$?

$$\theta = \$$theta_0$$ + \omega_{0z} t + \frac{1}{2} \alpha_z t^2$

Question 1

A flywheel has an angular position given by $$	heta = (2\ \mathrm{rad}/\mathrm{s}^3)t^3$. What is the instantaneous angular velocity at t = 2$$\ \mathrm{s}$$?

Accepted Answer

$$\omega = 12\ \mathrm{rad}/\mathrm{s}$$

Question 2

A point on the rim of a rotating disk (radius $$0.18\ \mathrm{m}) $$moves through an angle of $$\pi/2$$ radians. What is the arc length $$s$$ traveled by the point?

Accepted Answer

$$s = 0.09\pi\ \mathrm{m}$$

Question 3

A centrifuge spins at a constant angular velocity. A point $$0.10\ \mathrm{m}$$ from the axis moves at $$150\ \mathrm{m/s}. $$What is the angular velocity $$\omega$$?

Accepted Answer

$$\omega = 1500\ \mathrm{rad}/\mathrm{s}$$

Question 4

Which of the following is the correct relationship between linear speed $$v$$ and angular speed $$\omega$$ for a point at distance $$r$$ from the axis?

Accepted Answer

$$v = r\omega$$

Question 5

A Blu-ray disc slows from $$27.5\ \mathrm{rad}/\mathrm{s} to $$rest with a constant angular acceleration of $$-10\ \mathrm{rad}/\mathrm{s}^2. $$What is its angular velocity after $$0.3\ \mathrm{s}$$?

Accepted Answer

$$\omega = 26.9\ \mathrm{rad}/\mathrm{s}$$

Question 6

If a point on a rotating rigid body is twice as far from the axis as another point, how do their linear and angular speeds compare?

Accepted Answer

The farther point has twice the linear speed; angular speeds are equal.

Question 7

A rotating wheel has an angular acceleration $$\alpha_z = 2\ \mathrm{rad}/\mathrm{s}^2$$ and an initial angular velocity $$\omega_{0z} = 3\ \mathrm{rad}/\mathrm{s}. $$What is its angular velocity after $$4\ \mathrm{s}$$?

Accepted Answer

$$\omega_z = 11\ \mathrm{rad}/\mathrm{s}$$

Question 8

A point $$0.10\ \mathrm{m}$$ from the axis of a centrifuge moves at $$150\ \mathrm{m/s}. $$What is its radial (centripetal) acceleration?

Accepted Answer

$$a_{rad} = 225000\ \mathrm{m}/\mathrm{s}^2$$

Question 9

Which equation correctly gives the angular displacement $$	heta$$ for a body with constant angular acceleration $$\alpha_z$$ and initial angular velocity $$\omega_{0z}$$?

Accepted Answer

$$	heta = \$$theta_0$$ + \omega_{0z} t + \frac{1}{2} \alpha_z t^2$

Question 10

A watch's second hand rotates at a constant rate. What are its angular velocity $$\omega_z$$ and angular acceleration $$\alpha_z$$?

Accepted Answer

$$\omega_z = -2\pi\ \mathrm{rad}/\mathrm{min},\ \alpha_z = 0$$

Question 11

A rotating disk starts from rest and accelerates at $$4\ \mathrm{rad}/\mathrm{s}^2. $$How many radians does it rotate through in $$3\ \mathrm{s}$$?

Accepted Answer

$$	heta = 18\ \mathrm{rad}$$

Question 12

If $$	heta is $$measured in radians, $$s is $$arc length, and $$r is $$radius, which equation is correct?

Accepted Answer

$$	heta = \frac{s}{r}$$

Question 13

A wheel rotates $$10$$ times. What is the total angle in radians through which it rotates?

Accepted Answer

$$20\pi$$ radians

Question 14

A point on a rotating disk has a tangential acceleration $$a_{tan} = r\alpha. If$$ $$r = 0.2\ \mathrm{m}$$ and $$\alpha = 5\ \mathrm{rad}/\mathrm{s}^2$$, what is $$a_{tan}$$?

Accepted Answer

$$a_{tan} = 1\ \mathrm{m}/\mathrm{s}^2$$

Question 15

A wheel rotates with constant angular acceleration. Which equation gives its angular velocity after time $$t$$?

Accepted Answer

$$\omega_z = \omega_{0z} + \alpha_z t$$

Question 16

A car tire has a radius of $$0.3\ \mathrm{m}$$ and rotates at $$10\ \mathrm{rad}/\mathrm{s}. $$What is the linear speed of a point on the edge?

Accepted Answer

$$v = 3\ \mathrm{m}/\mathrm{s}$$

Question 17

A rotating object has $$\omega_{0z} = 5\ \mathrm{rad}/\mathrm{s}$$, $$\alpha_z = -2\ \mathrm{rad}/\mathrm{s}^2. $$How long until it stops?

Accepted Answer

$$t = 2.5\ \mathrm{s}$$

Rotation of Rigid Bodies: Angular Kinematics and Dynamics

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