1. Circular Motion

2. Agenda Introduction Qualitative Understanding Prerequisites
Examples and Non-examples of Circular Motion
Qualitative Understanding
Demo
Centripetal force
Linear velocity

3. Agenda Quantitative Understanding Examples Angular measure in radians
Angular velocity
Centripetal acceleration & force
Examples
Tension in the string
Conical pendulum
Car going round a bend
Cyclist going round a corner
Airplane turning in a circular path in a horizontal plane
Vertical circular motion 1
Vertical circular motion 2

4. Prerequisites Kinematics & Dynamics Types of forces
Newton’s laws of motion
Free body diagram
Types of forces
Weight
Tension
Friction
Normal
Elementary calculus
Limits & derivatives

5. Example: Car rounding a bend

6. Example: Car rounding a bend

7. Example: Roller Coaster

8. Example: Satellite

9. Example: Solar System ?

10. Non-examples
Most planetary orbits are not perfectly circular – they are elliptical.
However, sometimes we can approximate the ellipse as a circle when we perform calculations.
Internal rotation is also a non-example of the circular motion that we are learning in this lecture.

11. Demo 1: horizontal circular motion
Normal, N1
Normal, N2
Weight, mg

12. Demo 1: horizontal circular motion
Normal, N2
Normal, N2
Normal, N2

13. Demo 2: conical pendulum
Tension, T Ty Tx
Weight, mg

14. Centripetal force
In both examples, there is a net force acting on the object in a direction towards the centre of the circle.
This net force keeps the object in the circular path.
This net force is called the centripetal force.

15. Linear velocity
If the centripetal force is suddenly removed, the object will go off tangentially, i.e. no more circular motion!
This is because the instantaneous linear velocity of the object is pointing in the tangential direction.
Thus it is also called the tangential velocity.

16. Centripetal acceleration & linear velocity
The centripetal force produces an acceleration towards the centre.
This acceleration is changing the direction of the linear velocity, so as to keep the object in the circle.

17. Back to the whiteboard…
Quantitative Understanding
Angular measure in radians
Angular velocity
Centripetal acceleration & force
Examples
Tension in the string
Conical pendulum
Car going round a bend
Cyclist going round a corner
Airplane turning in a circular path in a horizontal plane
Vertical circular motion 1
Vertical circular motion 2