## Wednesday, January 13, 2016

### Angular Displacement ,Angular Velocity and Angular Acceleration

Angular displacement is the angle made by the body about the axis of rotation when the body is in rotational motion. If a body is rotating about a fixed axis, then it is said to be in rotational motion. Each particle of the body will have different displacement with respect to the axis of rotation.

Each particle has its own displacement and it is different for each particle. We cannot treat any of the particle as the displacement of the system. We cannot study rotational motion in terms of translatory motion as explained in the previous video lesson. To understand rotational motion we need different set of physical quantities.

In traslatory motion, we have displacement and it is defined as the shortest distance between initial and final positions of a body. Similarly in rotational motion, we have angular displacement. Though each particle in rotation, has different kinds of displacement, all of them has same angular displacement with respect to the axis of rotation. Hence we can study this kind of motion using angular displacement. It is measured with a unit called radian and it has no dimensional formula. It is the ratio of similar physical quantities and hence it has no dimensions.

Angular displacement is defined as the ratio of arc and radius of circular motion.At a position, all particles in circular motion will be having the same angular displacement. This is explained well in detail in the following video lesson.

Angular Velocity

Angular velocity is defined as the rate of change of angular displacement. It is similar to velocity of translatory motion. Velocity is defined as rate of change of displacement. We can say that angular displacement divided by the time as angular velocity. It is measured with a unit called radian per second.

We can find the relation between linear and angular velocity as shown in the below video lesson.

It can be proved that the linear velocity as the cross product of radius vector and angular velocity. If we multiply two vectors and the result is also a vector then that kind of multiplication is called cross product of the two vector. Two find the direction of this cross product, we can use right hand thumb rule or cork screw rule.

Angular Acceleration

Angular acceleration is defined as the rate of change of angular velocity. It is similar to linear acceleration of translatory motion. This acceleration is also called as tangential acceleration. This will change the velocity of the body at each point changes.If a body is not having any angular acceleration and still in rotational motion, then it is said to be uniform circular motion.

We can find the relation between linear and angular accelerations as shown in the video lesson below.

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