Physics circular motion

Newtons 1st law

all moving objects will continue in motion in the same direction unless a net force acts upon the object to deviate its motion from a straight line path

centripetal force

A net force directed towards the centre of the circle to allow it to move along a circular path

centripetal acceleration

the acceleration produced by centripetal force

newtons 2nd law

The net force acting on an object must be in the same direction as the acceleration

Uniform circular motion

• magnitude of velocity of object stays constant while direction is always changing

• Velocity is changing with time, therefore object is accelerating and must experience a net force

• Since velocity is tangent to the circular path at every instant in time, and direction of velocity changes and not magnitude, the change in velocity hence acceleration must be directed perpendicularly to the velocity and towards the centre of the circle at every instant in time

• Net force acting on the object must be in the same direction as the acceleration and since net force acts towards the centre of the circle, there is centripetal force. The acceleration produced by the force is centripetal acceleration

Work done by centripetal force

• for object in circular motion, velocity is directed tangent to the circle , while centripetal force acts radially inwards

• Hence centripetal force is always directed perpendicular to the direction of the objects change in displacement

• Since displacement moved along line of action of centripetal force is 0, work done is 0

angular displacement

The angle through which an object turns in a specified direction about a specified axis

angular velocity

Rate of change of angular displacement with respect to time of the angular direction of the line joining an object to the axis about which it is rotating, in a given direction

why does object experience a force in circular motion

• though object is moving at constant speed, its velocity is always changing as direction of motion is constantly changing. this object experiences acceleration and force acts since F=ma

why is the force directed towards the centre of the circle/ perpendicular to the motion of object

as the object is moving at constant speed, there must be no component of force in the direction of motion of object. otherwise speed will change. therefore direction of force has to be perpendicular to the direction of motion