# Rotational Dynamics

## Angular Momentum

Angular momentum is the moment of linear momentum. It defines the quantity of motion of rigid rotational bodies. Angular momentum is defined as the vector product( or cross product) of distance from the axis of rotation with the linear momentum

## Work done by couple

Consider a wheel of radius ‘r’ rotating about an axis through a center due to the application of a couple of magnitude ‘F’ at points A and B. ## Torque in rotational motion

We know about the definition of force in linear motion as an external agent to change the state of rest or of uniform motion in a straight line according to Newton’s first law of motion. Similarly, the rotating force is required to change the state of rest or of uniform motion in a circular motion and that rotating force is called torque. ## Calculation of Moment of Inertia in different bodies

1] Moment of Inertia of the thin rod about an axis perpendicular to its plane and passing through a center. Let us consider a thin uniform rod of mass ‘M’ and length ‘L’ rotating about a perpendicular axis and passing through a center. Consider a small element of thickness ‘dx’ of mass ‘dm’ at a … ## Theorem on the Moment of Inertia

There are two theorems on a moment of inertia that helps to calculate the moment of inertia of any rigid body. They are:
This theorem states that the moment of inertia of a plane lamina about a perpendicular axis to the plane lamina is equal to the sum of the moment of inertia of plane lamina under two axes on a plane right angle to each other and intersecting at a point through which a perpendicular axis passes.