Q: Which formula gives the angular displacement $$\Delta \theta$$ for a particle moving with constant angular acceleration $$\alpha$$ over time $$t$$?

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

Q: Which equation correctly expresses the average angular velocity $$\omega_{avg}$$ over a time interval $$\Delta t$$?

$$\omega_{avg} = \frac{\Delta \theta}{\Delta t}$$

Question 1

A particle moves along a circular path of radius $$r at a $$constant angular velocity $$\omega. $$What is the formula for its tangential velocity $$v_t$$?

Accepted Answer

$$v_t = \omega r$$

Question 2

Which of the following best describes centripetal acceleration for an object in uniform circular motion?

Accepted Answer

It is directed toward the center of the circle and has constant magnitude.

Question 3

A Ferris wheel has a radius of $$9.0\ \mathrm{m}$$ and rotates at $$2.0\ \mathrm{rpm}. $$What is the centripetal acceleration experienced by a rider?

Accepted Answer

$$a_c = 0.39\ \mathrm{m/s^2$}$$

Question 4

If a fan is spinning at $$60\ \mathrm{rpm}$$ and coasts to a stop in $$25\ \mathrm{s}$$ with constant angular acceleration, how many revolutions does it make before stopping?

Accepted Answer

$$12.5$$

Question 5

Which equation correctly relates centripetal acceleration $$a_c to $$angular velocity $$\omega$$ and radius $$r$$?

Accepted Answer

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

Question 6

Two people are riding a merry-go-round. Sam is twice as far from the axis as Rasheed. If the angular velocity is the same for both, what is the ratio of Sam's tangential velocity to Rasheed's?

Accepted Answer

Sam's tangential velocity is twice Rasheed's.

Question 7

Which of the following statements about reference frames is correct?

Accepted Answer

Velocity of an object depends on the observer's reference frame.

Question 8

A particle moves in a circle with increasing speed. Which component of acceleration is responsible for the change in speed?

Accepted Answer

Tangential acceleration

Question 9

Which formula gives the angular displacement $$\Delta 	heta$$ for a particle moving with constant angular acceleration $$\alpha$$ over time $$t$$?

Accepted Answer

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

Question 10

A rotating wheel slows down with a constant angular acceleration. If its initial angular velocity is positive, what is the sign of its angular acceleration?

Accepted Answer

Negative

Question 11

Which of the following is NOT a contact force?

Accepted Answer

Gravity acting on a coffee mug

Question 12

A cyclist moves at $$5\ \mathrm{m/s}$$ relative to the ground. A car moves at $$15\ \mathrm{m/s} in $$the same direction. What is the velocity of the car relative to the cyclist?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 13

Which equation correctly expresses the average angular velocity $$\omega_{avg}$$ over a time interval $$\Delta t$$?

Accepted Answer

$$\omega_{avg} = \frac{\Delta 	heta}{\Delta t}$$

Question 14

A paperclip jumps up to stick to a magnet. What type of force is responsible for this interaction?

Accepted Answer

Non-contact force

Question 15

If the angular velocity $$\omega of a $$wheel is changing with time, which quantity describes the rate of change of $$\omega$$?

Accepted Answer

Angular acceleration $$\alpha$$

Question 16

Which of the following is true about centripetal acceleration in non-uniform circular motion?

Accepted Answer

It always points toward the center, but its magnitude may change.

Question 17

A wheel rotates with constant angular acceleration $$\alpha. $$Which equation gives its angular velocity $$\omega$$ after time $$t if $$its initial angular velocity is $$\omega_i$$?

Accepted Answer

$$\omega = \omega_i + \alpha t$$

Question 18

Which of the following best describes a force in physics?

Accepted Answer

A push or pull that acts on an object and has both magnitude and direction.

Question 19

A ball is attached to a string and swung in a horizontal circle at constant speed. What is the direction of the net force acting on the ball?

Accepted Answer

Toward the center of the circle

Circular Motion: Position, Velocity, Acceleration, and Reference Frames

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