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Circular Motion

Circular Motion. Agenda. Introduction Prerequisites Examples and Non-examples of Circular Motion Qualitative Understanding Demo Centripetal force Linear velocity. Agenda. Quantitative Understanding Angular measure in radians Angular velocity Centripetal acceleration & force Examples

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Circular Motion

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  1. Circular Motion

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

  3. Agenda • 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

  4. Prerequisites • Kinematics & Dynamics • 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. Tension, T Ty Tx Demo 2: conical pendulum 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

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