Post on 13-Jan-2016
transcript
Circular Motion
What is a circular motion ?
• Motion along a circular path / arc.
Uniform Circular Motion
• Circular motion with constant speed.
Non-uniform Circular Motion
• Circular motion with changing speed
Circular Motion … Examples
– Earth moving around the Sun– Electron moving around a proton in a
hydrogen atom.– Moving car in a roundabout.– Simple pendulum.
Circular Motion … Periodic Motion
distance = rate time
time =distance
rate v
T =2 r
v
2
r
Periodic Motion :Motion that repeat itself after a fixed time.
Period : Time of one “cycle”.
Is the ball accelerating ?
When the string breaks . . .
The string breaks at this position
The object then moves along a straight line.
Without tension the object moves in a straight line.
Tension changes the direction of the object.
Circular Motion … Accelerating Motion
• Object moves along a circular path.• The direction of velocity is changing.• Changing velocity implies that the object accelerates.
Magnitude :
Centripetal Acceleration
rr
va 2
2
Direction : Towards the centre
Q: Is the acceleration a constant?
Centripetal Acceleration . . . Proof
s vv
v
rt
r
tv
r
s
r
v
t
v
dt
dva
2
Centripetal Acceleration . . . Proof
s
90
2
180 limφ lim
2
180φ
0Δθ0Δθ
F ma
Fmv
r
2
Centripetal Force
Centripetal Force
• When an object moves in a circle, it must accelerates.• The acceleration directs toward the centre of the circle.• According to Newton’s 2nd law, there has to be a force
to produce such acceleration• This force must point toward the centre of the circle
(Centripetal Force)
Origin of Centripetal Force
Circular Motion Centripetal Force
Satellite in orbit around Earth Gravitational force of the Earth
Car moving around a flat-curve Static frictional force
Car moving around a banked-exitStatic frictional force and normal force
Toy-plane tied to a rope and moving in a circle
Tension in the rope
Astronaut in a rotating space station
Normal force by the surface/floor
Rider at a roller coaster weight and/or normal force