## Homework Helpers: Physics

**4 Rotational and Circular Motion**

**Chapter 4 Examination**

**Part I—Matching**

Match the following terms to the definitions that follow.

a. radian

b. torque

c. period

d. rotational motion

e. centripetal force

f. centripetal acceleration

g. hertz

h. frequency

i. circular motion

_______1.__ The amount of time it takes to complete one vibration or one cycle of motion.

_______2.__ The motion of a body along a circular path.

_______3.__ A unit of angular measurement that is equal to 57.3°.

_______4.__ A unit that is equal to s^{–1}.

_______5.__ The ability of an applied force to produce rotational motion.

**Part II—Multiple Choice**

For each of the following questions, select the best answer.

__6.__ Which of the following angles is equal to approximately 2.00 radians?

a) 28.7°

b) 57.3°

c) 115°

d) 360°

__7.__ Convert 325° to radians.

a) 5.67 rad

b) 3.43 rad

c) 1.11 rad

d) 0.065 rad

__8.__ The car of a Ferris wheel travels an arc length of 6.80 m. If the radius of the wheel is 5.25 m, what is the angular displacement of the car?

a) 0.772 rad

b) 1.30 rad

c) 1.55 rad

d) 12.1 rad

__9.__ A bicycle tire is spinning with an angular velocity of 11.5 rad/s. How long would it take for a rock on the edge of the tire to experience an angular displacement of 4.50 rad?

a) 0.391 s

b) 2.56 s

c) 7.00 s

d) 51.8 s

__10.__ A boy spins a yo-yo over his head with a uniform angular velocity of 7.85 rad/s. If the radius of the circular path is 0.350 m, find the tangential speed of the yo-yo.

a) 22.4 m/s

b) 8.20 m/s

c) 7.50 m/s

d) 2.75 m/s

__11.__ A bug sitting 0.025 m from the center of a CD experiences a centripetal acceleration of 5.0 m/s^{2}. What is the bug’s tangential speed?

a) 0.354 m/s

b) 0.125 m/s

c) 200. m/s

d) 5.025 m/s

__12.__ A boy sitting 0.45 m from the center of a merry-go-round experiences a centripetal acceleration of 4.5 m/s^{2}. Find his angular speed.

a) 5.0 rad/s

b) 10.0 rad/s

c) 3.2 rad/s

d) 4.1 rad/s

__13.__ Two objects separated by a distance of d experience a force of F due to gravity. If the distance between the objects is tripled, what would be the new gravitational force between them?

a) 3F

c) 9F

__14.__ Two objects separated by a distance of 0.025 m experience a force of 4.3 × 10^{–6} N due to gravity. If the mass of the first object is 35.0 kg, find the mass of the second object.

a) 7.7 kg

b) 1.2 kg

c) 3.8 kg

d) 4.4 kg

**Part III—Calculations**

Perform each of the following calculations.

__15.__ If a girl sits 1.35 m from the center of a carousel with an angular speed of 3.89 rad/s, what is the centripetal acceleration she experiences?

__16.__ A uniform meter stick is balanced on a pivot point at the 50.0 cm mark. A 1.0 N weight is hung from the 20.0 cm mark. Another weight will be hung at the 70.0 cm mark in order to establish rotational equilibrium when the meter stick is horizontal. What should the magnitude of this second weight be?

__17.__ What is the period of a wave with a frequency of 5.0 × 10^{–3} Hz?

__18.__ Calculate the centripetal force acting on a 0.445 kg toy being spun in uniform horizontal circles with a radius of 0.875 m and a period of 1.20 seconds.

__19.__ Mars has a mass of approximately 6.421 × 10^{23} kg and a radius of approximately 3.397 × 10^{6} m. How much would a man with a mass of 80.0 kg weigh on Mars?

__20.__ Calculate the gravitational force of attraction between a 1.5 × 10^{3} kg car and a 50.0 kg woman separated by a distance of 1.3 m.