Circular Motion

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Circular Measure

In physics radians is used to measure angles. Theta is a ratio of lengths, with the unit rad.

Angular displacement measures how far an object has rotated.

Angular velocity, w (omega), is used to measure the rate of angular rotation. It is measured in radians per second.

The angular velocity can be connected to the time period with the following equation:

This can be linked to velocity:

This equation shows that rotational speed is faster further from the centre. For example, children on a roundabout have the same angular velocity, but the ones on the edge are moving faster.

Centripetal Acceleration

A particle is moving round a circular path at constant speed, and since it is continually changing direction it is always accelerating.

Velocity is a vector quantity, so if the directions of motion changes, there must be acceleration.

As a particle moves round a circular path, there is acceleration towards the centre of the circle, which is called centripetal acceleration. Since the acceleration is at right angles, there is no speeding up, just change in direction.

Size of acceleration is calculated by:

Centripetal Force

When an object moves around a circular path, there must be a centripetal force acting towards the centre of the circle. Something must provide this force, such as a pull from a string or push from the road.

Where R is the unbalanced centripetal force:

The centripetal force does not exist because something is moving round a curved path, according to Newton's 2nd Law, to make something change direction a force is required to accelerate the object.