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Circular Motion
Agenda
1.
Introduction


2.
Prerequisites
Examples and Non-examples of Circular Motion
Qualitative Understanding

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
Demo
Centripetal force
Linear velocity
Agenda
3.
Quantitative Understanding



4.
Angular measure in radians
Angular velocity
Centripetal acceleration & force
Examples
1)
2)
3)
4)
5)
6)
7)
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
Prerequisites

Kinematics & Dynamics



Types of forces





Newton’s laws of motion
Free body diagram
Weight
Tension
Friction
Normal
Elementary calculus

Limits & derivatives
Example: Car rounding a bend
Example: Car rounding a bend
Example: Roller Coaster
Example: Satellite
Example: Solar System ?
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.
Demo 1:
horizontal circular motion
Normal, N1
Normal, N2
Weight, mg
Demo 1:
horizontal circular motion
Normal, N2
Normal, N2
Normal, N2
Demo 2: conical pendulum
Ty
Tension, T
Tx
Weight, mg
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.
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.
Centripetal acceleration
& linear velocity
1. The centripetal force
produces an
acceleration towards
the centre.
2. This acceleration is
changing the direction
of the linear velocity,
so as to keep the
object in the circle.
Back to the whiteboard…
3.
Quantitative Understanding



4.
Angular measure in radians
Angular velocity
Centripetal acceleration & force
Examples
1)
2)
3)
4)
5)
6)
7)
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