Circular Motion

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

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

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

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 Tension, T Ty 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 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.

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