Q: Which of the following is NOT a correct rotational analogue to linear motion?

Torque $$\tau$$ corresponds to momentum $$p$$

Q: A car is turning a corner on a wet road with $$\mu_s = 0.5. If $$the radius of the turn is $$50\,\text{m}$$ and $$g = 9.8\,\text{m/s}^2$$, what is the maximum speed before sliding occurs?

$$v_{max} = \sqrt{0.5 \times 9.8 \times 50} = 15.7\,\text{m/s}$$

Question 1

Which equation correctly relates the tangential velocity $$v_t to $$the angular velocity $$\omega$$ and radius $$r$$ for an object in circular motion?

Accepted Answer

$$v_t = r \omega$$

Question 2

A particle moves in a circle of radius $$r at $$constant speed. What is the direction of its acceleration vector?

Accepted Answer

Inward toward the center

Question 3

If a car of mass $$m$$ turns a corner of radius $$r on a $$level road, what force provides the centripetal acceleration?

Accepted Answer

Static friction

Question 4

What is the formula for the maximum speed $$v_{max} a $$car can take a turn of radius $$r$$ without sliding, given the coefficient of static friction $$\mu_s$$ and gravitational acceleration $$g$$?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r}$$

Question 5

If Roger is riding a merry-go-round at radius $$R/2$$ and Sarah at radius $$R$$, how does Sarah’s centripetal acceleration compare to Roger’s?

Accepted Answer

Four times as large

Question 6

Which of the following is NOT a correct rotational analogue to linear motion?

Accepted Answer

Torque $$	au$$ corresponds to momentum $$p$$

Question 7

A hockey puck is tied to a stake and swung in a circle on frictionless ice. What force acts on the puck to keep it moving in a circle?

Accepted Answer

One or more forces pulling inward

Question 8

For uniform circular motion, which component of acceleration is nonzero?

Accepted Answer

Radial component $$a_{r}$$

Question 9

What is the correct expression for centripetal acceleration $$a_r in $$terms of tangential velocity $$v$$ and radius $$r$$?

Accepted Answer

$$a_r = v^2$ / r$$

Question 10

Which equation correctly relates angular velocity $$\omega to $$tangential velocity $$v$$ and radius $$r$$?

Accepted Answer

$$\omega = v / r$$

Question 11

A car is turning a corner on a wet road with $$\mu_s = 0.5. If $$the radius of the turn is $$50\,	ext{m}$$ and $$g = 9.8\,	ext{m/s}^2$$, what is the maximum speed before sliding occurs?

Accepted Answer

$$v_{max} = \sqrt{0.5 	imes 9.8 	imes 50} = 15.7\,	ext{m/s}$$

Question 12

Which of the following statements about centripetal force is correct?

Accepted Answer

Centripetal force is provided by familiar forces such as friction or tension

Question 13

If an object moves in a circle at constant speed, what happens to its velocity vector?

Accepted Answer

Its direction changes but magnitude remains constant

Question 14

Which equation represents the work done by a force $$\vec{F}$$ over a displacement $$\vec{dr}$$?

Accepted Answer

$$W = \int \vec{F} \cdot \vec{dr}$$

Question 15

A merry-go-round spins at constant angular velocity $$\omega. If $$Bob is at radius $$R/2$$ and Alice at radius $$R$$, what is the angular velocity of Bob compared to Alice?

Accepted Answer

$$\omega_{R/2} = \omega_{R}$$

Question 16

Which of the following is the correct expression for rotational kinetic energy $$K_{rot} in $$terms of angular momentum $$L$$ and moment of inertia $$I$$?

Accepted Answer

$$K_{rot} = L^2$ / 2I$$

Question 17

Which law describes the relationship between net force and acceleration for linear motion?

Accepted Answer

Newton's 2nd Law: $$F_{net} = ma$$

Question 18

In uniform circular motion, what is the net force in the tangential direction?

Accepted Answer

$$F_{net, t} = 0$$

Question 19

A particle in uniform circular motion has angular frequency $$\omega$$ and radius $$r. $$What is its tangential velocity?

Accepted Answer

$$v_t = \omega r$$

Circular Dynamics and Uniform Circular Motion

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