Force and Motion-II:
continued
Friction and Drag;Circular Motion
Lecture 6
Monday:2 February 2004
UNIFORM CIRCULAR
MOTION
CIRCULAR MOTION
• When an object travels in a circle, its velocity is constantly
changing (in direction-at least).
• That means the object has a non-zero acceleration even if it
moves at constant speed.
What is the direction of this
acceleration?
Acceleration in Circular Motion
Centripetal acceleration:
• Direction:
Toward the center of the circle
• Magnitude:
2
v
a
r
FORCES IN CIRCULAR
MOTION
• An “unbalanced” force must cause the
acceleration.
2


F  ma
v
a
r
and
2
v
F m
r
and the direction is toward the center.
Using Freebody Diagrams to
Analyze Forces
Twirl a ball attached to a string in a vertical circle. What forces
act on the ball and what are the direction of these forces?
Using Freebody Diagrams to
Analyze Forces
What forces act on the ball and what are the direction of these forces?
Top
a
T
Are we missing a force?
W
(the centripetal force)?
Is the acceleration =g?
Bottom
T
a
W
Using Freebody Diagrams to
Analyze Forces
What forces act on the ball and what are the direction of these forces?
Top
a
T
T+W=ma
W
Bottom
Is the acceleration =g?
T-W=ma
T
a
Are we missing a force?
(the centripetal force)?
-T-W=m(-a) or
W
Any force can be a “centripetal”
force.
-Gravitational
Attraction
-Tension in a
string
-Normal Force
-A push or pull…
Does the planet in orbit here have a gravitational force
AND a centripetal force acting on it?
PERIOD IN CIRCULAR
MOTION
Circumfera nce  2r
position
and Velocity 
time
2r
2r
v

time for one revolution
T
2r
so Period T 
v