Q: If a rotating object has both tangential acceleration $$a_t$$ and centripetal acceleration $$a_c$$, what is the total acceleration $$\vec{a}_{\text{total}}$$?

$$\vec{a}_{\text{total}} = \vec{a}_t + \vec{a}_c$$

Q: A point on the Earth's equator travels a distance equal to the circumference of the Earth in one day. If the Earth's radius is $$R_E = 6.37 \times 10^6$\,\mathrm{m}$$, what is the linear speed $$v at $$the equator?

$$v = 4.63 \times 10^2$\,\mathrm{m/s}$$

Q: A disk starts from rest and accelerates with a constant angular acceleration $$\alpha. $$After time $$t$$, what is its angular displacement $$\theta$$?

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

Question 1

A point on the rim of a rotating disk travels a distance $$s$$ along the circumference. If the disk rotates through an angular displacement $$	heta (in $$radians) and has a radius $$R$$, which equation correctly relates $$s$$, $$R$$, and $$	heta$$?

Accepted Answer

$$s = R 	heta$$

Question 2

A large wind turbine has blades of length $$R = 50\,\mathrm{m}$$ and rotates at $$f = 10\,\mathrm{RPM}. $$What is the angular speed $$\omega in$$ $$\mathrm{rad/s}$$?

Accepted Answer

$$\omega = 1.05\,\mathrm{rad/s}$$

Question 3

If the angular speed $$\omega of a $$rotating object is constant, what is the tangential acceleration $$a_t at a $$point a distance $$r$$ from the axis?

Accepted Answer

$$a_t = 0$$

Question 4

A steel ball rolls counterclockwise around a roulette wheel of radius $$R = 0.15\,\mathrm{m}$$, completing $$2$$ revolutions in $$1.25\,\mathrm{s}. $$What is its angular speed $$\omega$$?

Accepted Answer

$$\omega = 10.05\,\mathrm{rad/s}$$

Question 5

Which of the following best describes the direction of centripetal acceleration $$\vec{a}_c$$ for a point on a rotating rigid body?

Accepted Answer

It is always directed radially inward toward the center of rotation.

Question 6

The angular acceleration $$\alpha is $$defined as:

Accepted Answer

$$\alpha = \dfrac{\Delta \omega}{\Delta t}$$

Question 7

A point is located $$0.1\,\mathrm{m}$$ from the center of a shaft rotating at $$f = 50\,\mathrm{rev/s}. $$What is the linear speed $$v of $$the point?

Accepted Answer

$$v = 31.4\,\mathrm{m/s}$$

Question 8

Which equation correctly relates linear speed $$v to $$angular speed $$\omega$$ and radius $$r$$?

Accepted Answer

$$v = \omega r$$

Question 9

If a rotating object has both tangential acceleration $$a_t$$ and centripetal acceleration $$a_c$$, what is the total acceleration $$\vec{a}_{	ext{total}}$$?

Accepted Answer

$$\vec{a}_{	ext{total}} = \vec{a}_t + \vec{a}_c$$

Question 10

Which of the following is true about angular velocity $$\omega$$ for points on a rigid rotating body?

Accepted Answer

All points have the same angular velocity $$\omega.$$

Question 11

The equation $$	heta = \omega_i t + \frac{1}{2} \alpha t^2$ is analogous to which equation in linear motion?

Accepted Answer

$$x = v_i t + \frac{1}{2} a t^2$

Question 12

A point on the Earth's equator travels a distance equal to the circumference of the Earth in one day. If the Earth's radius is $$R_E = 6.37 	imes 10^6$\,\mathrm{m}$$, what is the linear speed $$v at $$the equator?

Accepted Answer

$$v = 4.63 	imes 10^2$\,\mathrm{m/s}$$

Question 13

If a rotating object has a constant angular acceleration $$\alpha$$, which equation gives the change in angular velocity $$\Delta \omega$$ after time $$t$$?

Accepted Answer

$$\Delta \omega = \alpha t$$

Question 14

A rotating object has an angular velocity $$\omega$$ and radius $$r. $$What is the formula for its centripetal acceleration $$a_c$$?

Accepted Answer

$$a_c = \$$omega^2$$ r$$

Question 15

Which of the following statements about tangential acceleration $$a_t is $$correct?

Accepted Answer

$$a_t is $$directed tangential to the circle and is present only if $$\omega is $$changing.

Question 16

A disk starts from rest and accelerates with a constant angular acceleration $$\alpha. $$After time $$t$$, what is its angular displacement $$	heta$$?

Accepted Answer

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

Question 17

If a point on a rotating object is at a distance $$r$$ from the axis and the object has an angular acceleration $$\alpha$$, what is the tangential acceleration $$a_t$$?

Accepted Answer

$$a_t = \alpha r$$

Question 18

Which of the following is NOT a correct analogy between linear and circular motion?

Accepted Answer

$$v \leftrightarrow 	heta$$

Angular Displacement, Speed, and Acceleration in Circular Motion

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