Q: The Earth orbits the Sun at a radius of $$R_E = 1.49 \times 10^8$ km and completes one revolution per year. What is the Earth's angular velocity $$\omega$$ in radians per second?

$$\omega = \frac{2\pi}{1\text{ yr}}$$

Q: A small steel ball rolls around the inside of a 2.0 m diameter roulette wheel, completing 2.0 revolutions in 1.2 seconds. What is its angular velocity $$\omega$$?

$$\omega = \frac{2\pi \times 2.0}{1.2}$$

Q: A car is driving on a banked curve with no friction. What is the correct expression for the banking angle $$\theta$$ required for the car to make the turn at speed $$v$$ and radius $$r$$?

$$\tan \theta = \frac{v^2$}{r g}$$

Question 1

A car travels around a circular track of radius $$r at a $$constant speed $$v. $$What is the correct expression for the car's centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 2

The Earth orbits the Sun at a radius of $$R_E = 1.49 	imes 10^8$ km and completes one revolution per year. What is the Earth's angular velocity $$\omega$$ in radians per second?

Accepted Answer

$$\omega = \frac{2\pi}{1	ext{ yr}}$$

Question 3

A small steel ball rolls around the inside of a 2.0 m diameter roulette wheel, completing 2.0 revolutions in 1.2 seconds. What is its angular velocity $$\omega$$?

Accepted Answer

$$\omega = \frac{2\pi 	imes 2.0}{1.2}$$

Question 4

Which of the following best describes the relationship between period $$T$$ and frequency $$f$$ for circular motion?

Accepted Answer

$$T = \frac{1}{f}$$

Question 5

A bucket of water (mass 5 kg) is swung in a vertical circle of radius 1 m. What is the tension in your arm at the bottom of the circle if the speed is $$v$$?

Accepted Answer

$$F_T = m v^2$ / r + m g$$

Question 6

In the Rotor ride, the minimum angular velocity $$\omega$$ required to keep a passenger from falling is given by which formula, if the coefficient of friction is $$\mu$$ and the radius is $$r$$?

Accepted Answer

$$\omega = \sqrt{\frac{g}{\mu r}}$$

Question 7

A car is driving on a banked curve with no friction. What is the correct expression for the banking angle $$	heta$$ required for the car to make the turn at speed $$v$$ and radius $$r$$?

Accepted Answer

$$	an 	heta = \frac{v^2$}{r g}$$

Question 8

Which of the following statements about centripetal force is correct?

Accepted Answer

Centripetal force is not a new force, but the net force causing circular motion.

Question 9

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

Accepted Answer

Toward the center of the circle

Question 10

If the frequency of rotation of a wheel is doubled, what happens to the centripetal acceleration of a point on the rim?

Accepted Answer

It increases by a factor of 4

Question 11

A car of mass $$m$$ travels at speed $$v$$ around a flat curve of radius $$r. $$What is the minimum coefficient of friction $$\mu$$ required to prevent skidding?

Accepted Answer

$$\mu = \frac{v^2$}{r g}$$

Question 12

A ball is attached to a string and swung in a horizontal circle. If the string breaks, what path will the ball follow?

Accepted Answer

It will move in a straight line tangent to the circle at the point of release.

Question 13

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

Accepted Answer

$$v = \omega r$$

Question 14

A roller coaster car of mass $$m$$ goes over the top of a circular hill of radius $$r at $$speed $$v. $$What is the normal force $$N$$ exerted by the track on the car at the top?

Accepted Answer

$$N = m g - m v^2$ / r$$

Question 15

A satellite orbits Earth in a circular path. Which force provides the required centripetal force?

Accepted Answer

Gravitational force

Question 16

A ball moves in a circle of radius $$r at $$constant angular velocity $$\omega. $$What is the formula for the distance traveled after time $$t$$?

Accepted Answer

$$s = \omega r t$$

Question 17

A car of mass $$m$$ travels at speed $$v$$ around a banked curve of radius $$r$$ with banking angle $$	heta. $$What is the correct expression for the normal force $$F_N$$ acting on the car?

Accepted Answer

$$F_N = m g / \cos 	heta$$

Circular Motion: Concepts, Equations, and Applications

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