**Circular Motion Practice Exercises
**(from Conceptual Physics by Hewitt)

1.
Marianne puts her favorite Backstreet Boys disc in her CD player.
If it spins with a frequency of 1800 revolutions per minute, what is the
period of spin of the compact disc?

2.
Hamlet, a hamster, runs on his exercise wheel, which turns around once
every 0.5s. What is the frequency
of the wheel?

3.
A sock stuck to the inside of the clothes dryer spins around the drum
once every 2.0 s at a distance of 0.50 m from the center of the drum.

a)
What is the sock’s linear speed?

b)
If the drum were twice as wide but continued to turn with the same
frequency, would the linear speed of the sock stuck to the inside be faster
than, slower than, or the same speed as your answer to part a?

4.
What is the radius of an automobile tire that turns with a frequency of
11 Hz and has a linear speed of 20.0 m/s?

5.
Luigi twirls a round piece of pizza dough overhead with a frequency of 60
revolutions per minute.

a)
Find the linear speed of a stray piece of pepperoni stuck on the dough 10
cm from the pizza’s center.

b)
In what direction will the pepperoni move if it flies off while the pizza
is spinning? Explain.

6.
Earth turns on its axis approximately once every 24 hours.
The radius of Earth is 6.38 x 10^{6} m.

a)
If some astronomical catastrophe suddenly brought Earth to a screeching
halt (a physical impossibility as far as we know), with what speed would Earth’s
inhabitants who live at the equator go flying off Earth’s surface?

b)Because Earth is solid, it must turn with the same frequency everywhere on its
surface. Compare your linear speed
at the equator to your linear speed while standing near one of the poles.

7.
Jessica is riding on a merry-go-round on an outer horse that sits at a
distance of 8.0 m from the center of the ride.
Jessica’s sister, Julie, is on an inner horse located 6.0 m from the
ride’s center. The merry-go-round
turns around once every 40.0 s.

a)
Explain which girl is moving with the greater linear speed.

b)
What is the centripetal acceleration of Julie and her horse?

8.
A cement mixer of radius 2.5 m turns with a frequency of 0.020 Hz.
What is the centripetal acceleration of a small piece of dried cement
stuck to the inside wall of the mixer?

9.
A popular trick of many physics teachers is to swing a pail of water
around in a vertical circle fast enough so that the water doesn’t spill out when
the pail is upside down. If Mr.
Lowell’s arm is 0.60 m long, what
is the minimum speed with which he can swing the pail so that the water doesn’t
spill out at the top of the path?

10.
To test their stamina, astronauts are subjected to many rigorous physical
tests before they fly in space. One
such test involves spinning the astronauts in a device called a centrifuge that
subjects them to accelerations far greater than gravity.
With what linear speed would an astronaut have to spin in order to
experience an acceleration of 3 *g*’s
at a radius of 10.0 m? (1 *g* = 10 m/s^{2})

11.
At the Fermilab particle accelerator in Batavia, Illinois, protons are
accelerated by electromagnets around a circular chamber of 1.00 km radius to
speeds near the speed of light before colliding with a target to produce
enormous amounts of energy. If a
proton is traveling at 10% the speed of light, how much centripetal force is
exerted by the electromagnets? (Hint:
The speed of light is 3.00 x 10^{8} m/s,
m_{p} = 1.67 x 10^{-27} kg)

12.
Roxanne is making a strawberry milkshake in her blender.
A tiny, 0.0050 kg strawberry is rapidly spun around the inside of the
container with a speed of 14.0 m/s, held by a centripetal force of 10.0 N.
What is the radius of the blender at this location?