newton’s 2nd law applied to circular motion
TRANSCRIPT
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Why do we study circular motions?
Circular motions are everywhere around us!!!
CD
Newton’s 2nd law applied to Circular Motion
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Why do we study circular motions?
Circular motions are everywhere around us!!!
How can we describe a circular motion?
What causes a circular motion?
Questions:
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Uniform circular motion
Constant speed, or, “constant magnitude” of velocity
Motion along a circle: “changing direction” of velocity
First, uniform circular motion
ice
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Does the velocity change in uniform circular motion? iClicker Quiz
(a) Yes
(b) No
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Acceleration is NOT zero!
Net force acting on the object is
NOT zero.
The “net” force in circular motion is
called “Centripetal force”.
Direction of velocity: changing
Yes, velocity changes
amFnet
Does the velocity change in uniform circular motion?
Centripetal force is simply a net force that gives rise to a
circular motion, NOT a new type of force.
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Acceleration
Magnitude:
Direction: toward center of circle
Uniform circular motion
Magnitude:
Direction: toward center of circle
Net force (“Centripetal force”) 2
netmv
Fr
netF
netF netF
Derivations of the above relations (see textbook)
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Example: Circular motion of a hanging ball
m=4.8 kg
2m 22 deg
Find the tension in the rope and the speed of the ball.
iClicker Quiz: What is the direction of acceleration when the ball is at the position in the figure?
(a) (b) (c)
(d) Out of plane (e) into plane
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Non-Uniform circular motion
Changing speed, or, changing magnitude of velocity
Motion along a circle: Changing direction of velocity
Example
Why do we study non-uniform
circular motion?
Some exciting motions
are non-uniform circular motions!
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Radial component of acceleration 2
r
va
r
Even for Non-Uniform circular motion,
Radial component of net force
2
r
vF m
r
Radial components follow the same relations
as uniform circular motions!
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iClicker Quiz
For the roller coaster, the magnitude of normal force at A is _______ mg.
(a) equal to (b) less than (c) greater than
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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.
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iClicker Quiz
For the roller coaster, the magnitude of normal force at B is _______ mg.
(a) equal to (b) less than (c) greater than
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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?
iClicker Quiz: At the bottom, the tension is ____ mg
(a) equal to (b) less than (c) greater than (d) not enough information !!!
2m