Rotational Motion

Defining Rotational Motion:When an object moves in circle. It is called rotational motion.For example:earth moves round the sun.

Rotational Motion consists of two types of motion:Translatory Motion and Rotatory Motion.

Translatory Motion:When objects changes its position with time .It is called translatory motion.Example: Running child.

Rotatory Motion:When an object moves about a fix axis in a circle.It is called rotatory motion.Example:Motion of wheels.

Rigid Body:A body which can't be deformed is called rigid body. Rigid body is one in which when distance between the particles remains same when body moces or changes its position.

In the rotational there is one of the main concept is Centre of Mass.Lets discuss about it.

Centre of Mass is the point in the rigid body where whole mass of the body is supposed to be concentrated.Centre of mass is not the mass but it is the position where mass of system is located.

Moment of Inertia: Monet of inertia is defined as the product of mass of particle with its distance from axis of rotation.

Here is the diagram:

In the above diagram particle of mass dm is located at a distance r from its axis of rotation .So its moment of inertia is as given by formula :

I = dm.r2

If we want to calculate the moment of inertia of whole system we need to sum of the moment of inertia of all particles.

Radius of Gyration :Radius of Gyration is the distance of centre of mass of body from its axis of rotation such that the moment of inertia of all particles should be remain same. It means you can calculate either moment of inertia by taking radius of gyration and multiplying it with centre of mass or you can calculate sum of moment of inertia of all particles.Both answers will be same.It is denoted by K.In the above diagram where is r we can assume K there to locate radius of gyration and dm there will be the position of centre of mass.

Torque:Turning effect of force is called torque.

Hey buddies all of you know about the force that it can changes the direction ,size and shape of particle on which it is applied but in case when one end of object is fixed and we apply force on the other end then this object starts moving about the fixed end . This turning effect is called torque. For example : door . One side of door is fixed with wall and we pull or push door from other side and door turns inside or outside. This turning effect is called torque. I hope now torque is understood by all with this example.

Torque is denoted by τ.

τ = r * F.