Chapter 5:
Circular Motion : TODAY
Universal Law of Gravitation: at the END of SEMESTER
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Newton’s 2nd law applied to Circular Motion of point particle
Why do we study circular motions?
Circular motions are everywhere around us!!!
CD
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Why do we study circular motions?
Circular motions are everywhere around us!!!
Questions:
How can we describe a circular motion?
What causes a circular motion?
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First, uniform circular motion
ice
Uniform circular motion
Constant speed, or,
“constant magnitude” of velocity
Motion along a circle:
“changing direction” of velocity
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iClicker Quiz
Does the velocity change in uniform circular motion?
(a) Yes
(b) No
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Does the velocity change in uniform circular motion?
 Direction of velocity: changing
 Yes, velocity changes
 Acceleration is NOT zero!


Fnet  m a
 Net force acting on the object is
NOT zero.
 The “net” force in circular motion is
called “Centripetal force”.
Centripetal force is simply a net force that gives rise to a
circular motion, NOT a new type of force.
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Uniform circular motion
Acceleration
(Note vT = v
for circular
motion)
Magnitude:
Direction: toward center of circle
Net force (“Centripetal force”)

mv 2
Fnet 
r
Magnitude:

Fnet

Fnet

Fnet
Direction: toward center of circle
Derivations of the above relations (see textbook)
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Example: Circular motion of a hanging ball
iClicker Quiz: What is the direction of acceleration
when the ball is at the position in the figure?
2m
(a)
22 deg
(b)
Find the tension in the rope and the speed
of the ball.
m=4.8 kg (c)
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Non-Uniform circular motion
Changing speed, or,
changing magnitude of velocity
Motion along a circle:
Changing direction of velocity
Why do we study non-uniform
circular motion?
Some exciting motions
are non-uniform circular motions!
Example 
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Even for Non-Uniform circular motion,
Radial component of acceleration
v2
ar 
r
(Note vT = v for circular motion)
Radial component of net force
v2
Fr  m
r
Radial components follow the same relations
as uniform circular motions!
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Example
A roller coaster of mass m=1000 kg is passing point A at 30 m/s.
Find the magnitude of normal force. We neglect friction force.
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Example
A roller coaster of mass m=1000 kg is passing point B.
Find the maximum speed it can have without losing contact with
the track.
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Example: A ball of mass 0.5 kg attached to a rope is rotating
in a vertical plane. What is the minimum speed the ball should have
at the top to prevent the rope from becoming loose?
2m
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