Question

Derive an expression for moment of force about a point.​

Answer 1

Answer:

• The moment of a force or torque is defined as the turning effect of the force about a pivot.

• It is the product of the force (F) and the perpendicular distance (d) from the line of action of the force to the pivot.

• Moment of force = d × F.

Answer 2

Answer:

Consider a mass m moving in a circle of radius r , acted on by a tangential force Ft as shown in Figure

Using Newton's second law to relate Ft to the tangential acceleration at = ralpha , where alpha is the angular acceleration:

Ft = mat

and the fact that the torque about the centre of rotation due to Ft is: tau = Ftr , we get = mr 2

For a rotating rigid body made up of a collection of masses m1,m2.... the total torque about the axis of rotation is:

The second line above uses the fact that the angular acceleration of all points in a rigid body is the same, so that it can be taken outside the summation.

Definition: Moment of Inertia of a rigid body

The moment of inertia, I , of a rigid body gives a measure of the amount of resistance a body has to changing its state of rotational motion. Mathematically,

The units of moment of inertia are kg cdot m 2.

Explanation:

hope it helps you