Unit 10
Academic Physics
Mr. Helzer
Name___________________
Circular Motion
1. Match the Linear/Tangential Motion in the far left column to its analogous Angular quantity in the
far right column.
Linear/Tangential Motion
Angular Motion
Linear/Tangential Acceleration
v2

Initial Angular Displacement
Initial Displacement
t
1
Final Angular Speed
Initial Speed
d2
2
Angular Acceleration
Finial Displacement
v1
1
Time
Time
d1
2
Final Angular Displacement
Final Speed
a
t
Initial Angular Speed
2. Match the angular quantity below to its appropriate name. Pay close attention to the units.

1
2
1
2
t
Initial Angular Displacement (rad)
Final Angular Speed (rad/s)
Angular Acceleration (rad/s2)
Time (rad/s)
Final Angular Displacement (rad)
Initial Angular Speed (rad/s)
a  r
v  r
s  r
3. The three equations above are known as the translational equations. They are used to translate
rotational quantities to _________________ quantities. Match the symbol to its name and appropriate
units.
Quantity
Name
Units
a
Arc Length/Tangential or Linear distance
Angular Displacement
Tangential/Linear Acceleration
Radius/Distance from Center of Rotation
Tangential/Linear Speed
Angular Acceleration
Angular Speed
rad/s
m
m/s
rad/s2
m
rad
m/s2


v
s
r

EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved.
Unit 6
1 of 7
1
2
 2  1  1t   t 2
22  12  2 2  1 
2  1   t

  2  1

t
t
4. On the figure to the right, label the “+” and “-“ signs
as they pertain to both linear motion and rotational
(angular) motion.
5. _____________ ____________is simply motion in which the path taken by a body forms a circular
pattern.
6. The rotation of a point on the outer edge of a rotating disk traces out a ___________________ wave.
7. The closer to the center the point is, the lower the _________________ of the corresponding wave.
8. Suppose we turned a CD through an angle  = 2.74 radians (157). How much linear distance would
a point travel that is located 5.0 cm from the CD’s center?
a  r
v  r
s  r
9. Conversions between angular quantities. 1 rev = ___________ degrees = __________ radians.
10. Convert 243 to revolutions and radians.
11. Convert 28.0 radians to revolutions and degrees.
12. Convert 110.0 revolutions to radians and degrees.
13. 4.25 rev = _______= ______ radians.
14. __________ rev = 1247.0 = ______ radians.
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved.
Unit 6
2 of 7
The two charts at the bottom of the page show the position v. time and
tangential distance of the bolts on the hub and the outer edge of the wheel.
Answer the questions below based upon these pictures.
15. How far from the wheels center are the hub bolts and the outer wheel
bolts located? Use the graphs below to answer this question.
16. Label the graphs on the charts below as “H” corresponding to the path
traced out by the bolts on the hub or as “O” corresponding to the path
traced out by the bolts on the outer edge of the wheel. Why did you label these graphs this way?
6
5
4
3
2
1
0
-1 0
-2
-3
-4
-5
-6
Distance v. Angle of Rotation
15
12.5
1
2
3
4
5
6
Distance (cm)
Position
Circular Motion
7
10
7.5
5
2.5
0
0
0.5
1
1.5
2
2.5
3
Angle of Rotation (Radians)
Time
17. If the angular speed of the wheel above is 5.0 rad/s, then what is the tangential speed of a bolt on the
hub and one at the outer edge of the wheel?
a  r
v  r
s  r
18. Suppose the wheel slowed from 5.0 rad/s to 1.8 rad/s in 4.5 seconds. What are the angular and
tangential accelerations of a bolt on the hub and one at the outer edge of the wheel?
Variable Value

1
2
1
2
t
1
2
 2  1  1t   t 2
22  12  2 2  1 
2  1   t
a  r
v  r
s  r
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved.
Unit 6
3 of 7
19. What is the tangential and angular displacement of a bolt on the hub and one at the outer edge of the
wheel from problems 15-18? Calculate the displacement that occurs for 4.5 s. (use the data in the table
from number 18)
20. A door is opened through an angle of 79 in 1.50 s. The screw on the hinge is 3.50 cm from the
hinge and the door knob is 85.0 cm from the hinge.
a. What is the tangential distance traveled by both the hinge and the knob?
b. What was the average angular velocity of both the hinge and the knob?
c. What was the average tangential speed of both the hinge and the knob?
Variable Value

1
2
1
2
t
1
2
 2  1  1t   t 2
22  12  2 2  1 
2  1   t
a  r
v  r
s  r
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved.
Unit 6
4 of 7
21. Dr. Physics pulls a log through his orchard. The diameter of the front wheel is df = 0.40 m and that
of the back wheel is db = 0.6 m. He accelerated from rest to a constant speed of 2.14 m/s in 1.43 s.
Afterwards, he pulled the log 400.00 m before beginning to come to a stop.
a. What was the angular acceleration of the wheels while he was accelerating?
b. What was the angular displacement of the wheels while he was accelerating?
c. What was the final angular velocity of the wheels at the end of the acceleration?
d. How many times did each wheel turn while traveling the 400.00 m?
Variable Value
a
v1
v2
d1
d2
t
1
2
 2  1  1t   t 2
22  12  2 2  1 
2  1   t
a  r
v  r
s  r
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved.
Unit 6
5 of 7
22. The blades (r = 0.4 m) in a box fan are initially rotating at 1500.0 RPM.
a. How many radians per second is this value?
b. How many meters per second is this value?
c. Once the switch on the fan is turned to the “Off” position, the blades take 37.0 s to come to a halt.
What is the angular acceleration of the blades while they are stopping? Tangential acceleration?
d. What is the angular displacement of the blades while they are stopping? Tangential distance?
Variable Value

1
2
1
2
t
1
2
 2  1  1t   t 2
22  12  2 2  1 
2  1   t
a  r
v  r
s  r
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved.
Unit 6
6 of 7
23. The large gear (d = 0.25 m) in a belt driven gear system
rotates at 55 RPM.
a. Would you expect the small gear to go faster or slower
than the large gear? Explain.
b. How does the tangential speed of the belt while moving around the Large gear compare to the
tangential speed of the belt while moving around the Small gear? Explain.
c. How fast is the small gear (d = 0.12 m) spinning at the same time (in m/s, rad/s, and RPM)?
a  r
v  r
s  r
EIMASES © 2001-2009 Mr. Shannon W. Helzer. All rights reserved.
Unit 6
7 of 7