Circular Motion. Agenda 1. Introduction Prerequisites Prerequisites Examples and Non-examples of...

Circular MotionCircular Motion

AgendaAgenda

1.1. IntroductionIntroduction PrerequisitesPrerequisites Examples and Non-examples of Circular MotionExamples and Non-examples of Circular Motion

2.2. Qualitative UnderstandingQualitative Understanding DemoDemo Centripetal forceCentripetal force Linear velocityLinear velocity

AgendaAgenda

3.3. Quantitative UnderstandingQuantitative Understanding Angular measure in radiansAngular measure in radians Angular velocityAngular velocity Centripetal acceleration & forceCentripetal acceleration & force

4.4. ExamplesExamples1)1) Tension in the stringTension in the string

2)2) Conical pendulumConical pendulum

3)3) Car going round a bendCar going round a bend

4)4) Cyclist going round a cornerCyclist going round a corner

5)5) Airplane turning in a circular path in a horizontal planeAirplane turning in a circular path in a horizontal plane

6)6) Vertical circular motion 1Vertical circular motion 1

7)7) Vertical circular motion 2Vertical circular motion 2

PrerequisitesPrerequisites

Kinematics & DynamicsKinematics & Dynamics Newton’s laws of motionNewton’s laws of motion Free body diagramFree body diagram

Types of forcesTypes of forces WeightWeight TensionTension FrictionFriction NormalNormal

Elementary calculusElementary calculusLimits & derivativesLimits & derivatives

Example: Car rounding a bendExample: Car rounding a bend

Example: Car rounding a bendExample: Car rounding a bend

Example: Roller CoasterExample: Roller Coaster

Example: SatelliteExample: Satellite

Example: Solar System ?Example: Solar System ?

Non-examplesNon-examples

Most planetary orbits are not perfectly circular – Most planetary orbits are not perfectly circular – they are they are ellipticalelliptical..

However, sometimes we can However, sometimes we can approximateapproximate the the ellipse as a circle when we perform calculations.ellipse as a circle when we perform calculations.

Internal rotationInternal rotation is also a non-example of the is also a non-example of the circular motion that we are learning in this circular motion that we are learning in this lecture.lecture.

Demo 1:Demo 1:horizontal circular motionhorizontal circular motion

Weight, Weight, mgmg

Normal, Normal, NN11

Normal, Normal, NN22

Demo 1:Demo 1:horizontal circular motionhorizontal circular motion

Normal, Normal, NN22

Normal, Normal, NN22

Normal, Normal, NN22

Demo 2: conical pendulumDemo 2: conical pendulum

Weight, Weight, mgmg

Tension, Tension, TTTTyy

TTxx

Centripetal forceCentripetal force

In both examples, there is a In both examples, there is a net forcenet force acting on acting on the object in a direction the object in a direction towards the centre of the towards the centre of the circlecircle..

This net force keeps the object in the circular This net force keeps the object in the circular path.path.

This net force is called the This net force is called the centripetal forcecentripetal force..

Linear velocityLinear velocity

If the centripetal force is If the centripetal force is suddenly removedsuddenly removed, the , the object will object will go off tangentiallygo off tangentially, i.e. no more , i.e. no more circular motion!circular motion!

This is because the This is because the instantaneous linear instantaneous linear velocityvelocity of the object is pointing in the tangential of the object is pointing in the tangential direction.direction.

Thus it is also called the Thus it is also called the tangential velocitytangential velocity..

Centripetal accelerationCentripetal acceleration& linear velocity& 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…Back to the whiteboard…

3.3. Quantitative UnderstandingQuantitative Understanding Angular measure in radiansAngular measure in radians Angular velocityAngular velocity Centripetal acceleration & forceCentripetal acceleration & force

4.4. ExamplesExamples1)1) Tension in the stringTension in the string

2)2) Conical pendulumConical pendulum

3)3) Car going round a bendCar going round a bend

4)4) Cyclist going round a cornerCyclist going round a corner

5)5) Airplane turning in a circular path in a horizontal planeAirplane turning in a circular path in a horizontal plane

6)6) Vertical circular motion 1Vertical circular motion 1

7)7) Vertical circular motion 2Vertical circular motion 2