# Rotational Dynamics

## Rotational Dynamics Multiple Choice Questions

Some multiple choice questions from rotational dynamics that includes core concept of this tipic.

## Rotational Dynamics Conceptual Questions

Rotational dynamics conceptual questions are important and gives you a lot of idea about a particular topic.

## Kinetic Energy and acceleration of a rolling body

The rolling body in an inclined plane has both rotational as well as translational motion as the body rotates as well as travels some distance in a straight line. The total kinetic energy of a rolling body can be found by adding its translational as well as rotational kinetic energy.

## 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.

## Kinetic Energy in rotational motion

In a similar way, the motion of a body in rotational motion also has kinetic energy. The kinetic energy in rotational motion is given by: $K.E = \frac{1}{2}I \omega^2$ where $I$ and $\omega$ are the moment of inertia and angular velocity of a body respectively.

## 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 …

## Moment of Inertia in different bodies

Different rigid bodies have different values of the moment of inertia and hence different formulas to calculate it. Also, the Moment of Inertia in a body depends upon the axis of rotation. So here is a table of moment of inertia in different bodies depending upon the axis of rotation.

## 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.