Circular motion

Introduction to circular motion

What is angular velocity?

What is angular velocity ?

As we have seen in this post an object undergoing circular motion has an angular displacement.

Hence the object will also have an angular velocity.

You will recall that velocity is the rate of change of displacement.

Let us look at an example of an object that is undergoing circular motion.

Fig 1                                              Fig 2                                                           

In fig 1 above a person moves in a circular path moving from A to B.

Thus the person can have an angular displacement θ in a time t.

We can thus calculate the angular velocity according to the equation below:

What if the person completes one complete turn?

Then the angular displacement will be 360^o or 2π rad.

The time taken to perform the complete turn will be the time period denoted by the letter T.

Thus the angular velocity will be calculated using the following equation:

Introduction to circular motion

Circular motion as the name suggest is the motion of an object in a circular path.Examples of circular motion is the motion of a car around a roundabout, a satellite around the earth or a stone tied to a string being whirled by the hand.

Centre of rotation

In fig 1 below you can see a circular path and a person is  moving in that circular path.

 

Fig 1

The person would move in such a way that at all time it would remain at the same distance from a point that we call the centre of  rotation. It is usually indicated by the symbol O in a diagram as you can see in fig 1.

Fig 2

Radius of circular path

As you can in Fig 2 I have draw the person at a point A and two other points B and C that the person would be during its motion later on. As is shown in the diagram the person would be at the same distance from the centre of rotation O. This distance is known as the radius of the circular path and is denoted by the letter r.

Angular displacement

In linear motion the movement is describe in term of the displacement of the object. In circular motion the movement of the object is describe in term of angular displacement. The angular displacement is simply the angle covered by the object during the circular motion.

Fig 3

In the first diagram of fig 3, you can see a person moves from point A to point B. In so doing it covers and angle θ of 120^o or 0.66 Pi rad. Hence the person would have an angular displacement of  120^o or 0.66 Pi rad. In the second motion the person starts from point A and moves along the circular path and finally back to A. In so doing the person covers an angle of 120^o or 2pi rad. Thus the angular displacement would be 120^o or 2pi rad