Download Mathematics of Circular Motion

Circular and Satellite Motion
Name: ___________________________
Mathematics of Circular Motion
Read from Lesson 2 of the Circular and Satellite Motion chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/circles/u6l2a.html
http://www.physicsclassroom.com/Class/circles/u6l2b.html
http://www.physicsclassroom.com/Class/circles/u6l2c.html
MOP Connection: Circular Motion and Gravitation: CG5
The verbal descriptions of physical situations and the corresponding free-body diagrams are given below. Use your
understanding of Newton's laws and centripetal force to fill in the blanks.
Free Body Diagram
Show your work or justify your answer
1. A 900-kg car is doing donuts in a parking lot with a
32-m diameter. The car does 10 revolutions in 80
Fnorm:
seconds.
Ffrict:
Fgrav:
v:
a:
Fnet:
2. A bucket of water (m=2.0 kg) is attached to a 0.80-m
long string and spun in a vertical circle. The speed of
the water at the bottom of the circular path is 6.0 m/s.
Ftens:
Fgrav:
a:
Fnet:
3. A 500-kg roller coaster car is at the top of the loop
on the Shockwave. The radius of the loop is 4.0 m
and the speed is 8.0 m/s.
Fgrav:
Fnorm:
a:
Fnet:
© The Physics Classroom, 2009
Circular and Satellite Motion
Name: ___________________________
4.
An object is moving in a circle and experiences centripetal acceleration. Sometime later, the velocity is doubled
while the radius stays the same. What happens to the acceleration? Explain.
5.
An object is moving in a circle and experiences centripetal acceleration. Sometime later, the acceleration is
doubled while the velocity remains the same, what must happen to the radius? Explain.
6.
An object is moving in a circle and experiences centripetal force. If mass, velocity and radius are all doubled,
what happens to the force? Explain.
7.
An object is moving in a circle and experiences centripetal acceleration. If mass is doubled while velocity and
radius remain the same, what happens to the acceleration? Explain.
8.
An object is moving in a circle and experiences centripetal acceleration. Sometime later, the velocity is tripled
while the radius is reduced by a factor of 2. What happens to the acceleration? Explain.
9.
A 500-kg roller coaster car is at the bottom of a loop on Flight Deck (previously Top Gun). The radius of the
loop is 20 m and the speed is 24 m/s.
a. Draw the FBD (with correct sizing and labels) for the box.
b.
Determine the following quantities. You must either show your work by identifying the equation used or
provide a written response to justify your answer.
m:
c.
a:
∑F:
Determine the magnitude (size) of each of your forces labeled in your free body diagram. For each force,
you must either show your work by identifying the equation used or provide a written response.
© The Physics Classroom, 2009