Physics 20 - Lesson 20
Vertical Uniform Circular Motion
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1.
Each free body diagram is worth 2 marks for a total of 12 marks.
A. Swinging on a rope, at lowest
position. No friction.
B. Tied to a post and moving in a circle
at constant speed on a frictionless
horizontal surface. Coming straight
FN
out of the paper.
FT
FT
Fg
Fg
C. Tied to point A by a string. Moving in a
horizontal circle at constant speed. Not
resting on a solid surface. No friction.
Coming straight out of the paper.
D. Swinging on a rope. No friction.
FT
FT
Fg
Fg
E. Swinging on a rope, at the top of a
vertical circle.
F. Riding on a horizontal disk that is rotating at
constant speed about its vertical axis. Friction
prevents rock from sliding. Rock is moving
straight out of the paper.
FN
Ff
FT
Fg
Fg
Dr. Ron Licht
Answer Key 20 - 1
www.structuredindependentlearning.com
Top
2)
r
Fg
7.0m
 3.5m
2
/5
Fc  Fg
m v2
 mg
r
v  gr  9.81 m s2 (3.5m)
v  5.86 m s
Top
3)
Fg
/4
Fc  Fg
m v2
 mg
r
v  gr  9.81 m s 2 (0.95m)
v  3.05 m s
4)
Bottom
FN  1960 N
•
/8
Fc  Fn  Fg
Fg
655 N
m

g 9.81m / s 2
m  66.8kg
Fc  1960 N  655 N
Fc  1305 N
Fg  655N
mv 2
r
Fc r
v
m
Fc 
v
1305 N 18.0m 
66.8kg
v  18.76m / s
The maximum tension occurs at
the bottom of the circle
5)
Bottom
/6
FT  186 N
•
Fc  186 N  14.7 N
Fc  171.3N
Fg  (1.50kg )(9.81 m s2 )
Fg  14.7 N
Dr. Ron Licht
Fc  FN  Fg
v
Fc r
(171.3N )(1.90m)

m
1.50kg
v  14.7 m / s
Answer Key 20 - 2
www.structuredindependentlearning.com
m  2.2kg
Top
6)
FT
Fg
/9
r  1.0m
T  0.97 s
Fg  mg
m 4 2 r
T2
2.2kg (4 2 )(1.0m)
Fc 
(0.97 s ) 2
Fc  92.3 N
Fc 
Fg  22kg (9.81 m s2 )
Fc  Fg  FT
Fg  21.6 N
FT  Fc  Fg
FT  92.3 N  21.6 N
FT  70.7 N
Bottom
FT
Fc  FT  Fg
•
FT  Fc  Fg
Fg  21.6 N
FT  92.3N  21.6 N
FT  113.9 N
Dr. Ron Licht
Answer Key 20 - 3
www.structuredindependentlearning.com