Question

Formula of velocity in revolutin per second in circular motion

Answer 1

The angular speed is how fast the angle (which I have labelled "a") changes. So it measures how fast the object is moving round the circle.

Angular speed is usually measured in radians per second (rad s-1), which is how many radians the particle moves through in a second. Alternatively, it can be measured in revolutions per second, which is how many complete circles the object moves through in a second.

There is a formula connecting "normal" speed (usually called "linear speed") and angular speed:

v = r w

where v is the linear speed, r is the radius of the circle and w is the angular speed.

Example

A particle is moving round a circle of radius 10cm. The angular speed is 2 rad s-1. Find the (linear) speed.

We want the radius in metres, which is 0.1m . Using the formula above, we get:

v = 0.1 × 2 = 0.2

So the speed is 0.2 m s-1 .

Note that if you are given the angular speed in terms of revolutions per second, you would have to convert to radians per second first. To do this, remember that 1 revolution per second is the same as 2p radians per second, because there are 2pradians in a circle.

Radial Acceleration

If a body is moving around a circle, even if it is moving at a constant speed it is accelerating. This is because it is changing direction (it isn't moving in a straight line).

The direction of this acceleration is towards the centre of the circle and the magnitude is given by:

a = v2/r

where v is the speed and r is the radius of the circle.

Using our formula above, this can also be written as:

a = r w2

Which of these you use will depend on whether you are dealing with speed or angular speed.

The acceleration occurs because there is a force acting:

Imagine that you are in a car going fast round a bend to the left. You will feel a force pulling you to one side (the left hand side). This is the force causing the acceleration. The force acts towards the centre of the circle.