Question

Derive a relation between torque applied and angular acceleration produced in a rigid body and hence define moment of inertia.

Answer 1

yh its relation is torque=moment of inertia×angular acceleration

moment of inertia is a analogue of mass of body which try to oppose rotational motion of a body.
I=mr sq

Answer 2

Torque = moment of inertia × angular acceleration

Explanation:

The relation between between torque applied and angular acceleration produced in a rigid body is given by :

$\tau=\dfrac{dL}{dt}$

Torque is equal to the rate of change of angular momentum.

$\tau=\dfrac{d(I\omega)}{dt}$

Since,

$\dfrac{d\omega}{dt}=\alpha$

Torque = moment of inertia × angular acceleration

In symbolic form, it is given by :

$\tau=I\alpha$

The point where the whole mass of the body is suppose to be concentrated is called its center of mass. The moment of inertia equal to the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. It can be calculated as :

$I=mr^2$

Learn more,

Center of mass

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