Dynamics of Rigid Bodies formulae for NEET

The rigid body is an idealization of a solid body where the deformations occurring on the body are neglected. In other words, the distance between any two given points of a rigid body remains a constant regardless of the external force acting upon it. The two types of motion a rigid body can undergo are;

  • Translational Motion
  • Rotational Motion

Moment of Inertia

Moment of Inertia is defined as the capacity of the system to oppose the change produced in the rotational motion of the body.

For a single particle moment of inertia I=mr2

Here m is the mass of the particle and r is the perpendicular distance from the axis about which moment of inertia is to be calculated.

For many particles, I = miri2

Moment of Inertia of different objects

moment of inertia for different objects

Radius of Gyration

K =

Here

M is the mass of the rotating object

I is the moment of inertia

Relation Between Torque and Moment of Inertia

Relation Between Torque and Moment of Inertia

τ is the torque (twisting effect of force)

I is the moment of inertia

α is the angular acceleration ( the rate of change of angular velocity)

Angular momentum

Angular momentum

angular momentum

Angular momentum of a rigid body rotating about a fixed axis

relation between angular momentum and moment of inertia

LH = angular momentum of the object about axis H

IH= Moment of inertia of rigid body about axis H

ω =angular velocity of the object

Relation between angular momentum and Torque

torque and angular momentum relation

Torque is the change in angular momentum