1. Circular Motion

2. 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

3. Circular Motion … Examples
Earth moving around the Sun
Electron moving around a proton in a hydrogen atom.
Moving car in a roundabout.
Simple pendulum.

4. Circular Motion … Periodic Motion
Motion that repeat itself after a fixed time.
Period : Time of one “cycle”.

5. Is the ball accelerating ?

6. 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.

7. Circular Motion … Accelerating Motion
Object moves along a circular path.
The direction of velocity is changing.
Changing velocity implies that the object accelerates.

8. Centripetal Acceleration
Magnitude :
Direction : Towards the centre
Q: Is the acceleration a constant?

9. Centripetal Acceleration . . . Proofs

10. Centripetal Acceleration . . . Proofs 

11. 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)
Centripetal Force

12. 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-exit
Static 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