Question

Define angular acceleration and torque. Establish the relation between angular acceleration and torque.

Answer 1

Angular acceleration : The rate of change of angular velocity is known as angular acceleration.
e.g., $\alpha=\frac{d\omega}{dt}$

torque : the rate of change of angular momentum is known as torque of the moment of force is known as torque.

Relation between angular acceleration and torque : consider a rigid body of mass M rotating in a circular path of radius R with angular velocity $\omega$ about fixed axis as shown in figure.
by definition of torque, $\tau=\frac{dL}{dt}=\frac{dI\omega}{dt}$

Where I is moment of inertia so, I = MR² [constant]
then, $\tau=I\frac{d\omega}{dt}$
But from definition of angular acceleration , $\alpha=\frac{d\omega}{dt}$
so, $\tau=I\alpha$.

Answer 2

Answer:

Angular acceleration : The rate of change of angular velocity is known as angular acceleration.

e.g.,

torque : the rate of change of angular momentum is known as torque of the moment of force is known as torque.

Relation between angular acceleration and torque : consider a rigid body of mass M rotating in a circular path of radius R with angular velocity  about fixed axis as shown in figure.

by definition of torque,

Where I is moment of inertia so, I = MR² [constant]

then,

But from definition of angular acceleration ,

so, .