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

Volume and volume of regular objects

The volume of an object is the space that the object occupies.

It is a scalar quantity and its SI unit is the cubic metre (m³)

The unit for the volume of object can also be derived from any other unit for length such as the cubic centimetre, cubic kilometre, etc

We are now going to see how the volume of an object is determined.  The method to determine the volume of the object depends on the nature of the object as shown below.

Volume of regular objects

Regular objects are those that have a plane of symmetry. It simply mean that if the object is cut along the plane of symmetry then the two parts will be similar to each other with the same volume.

The volume of regular objects is determined by measuring the dimensions of the object and finally using using an equation. The following are different regular objects and the equations used.

Cuboid

  

Cube

Volume = length * length * length

            = L³

Since all the sides of the cuboid are of equal length.   

Sphere

since r = d/2 then

As you can see all regular objects are determined by measuring the dimensions and then using equations to determine the volume. I would try with time to add as much of regular objects and their equations. If you require the equation for any regular shape then leave message in the comments below.