Question

Obtain expression for work and energy for rotational motion

Answer 1

Answer:

work and energy are essential

Answer 2

Concept

The work-energy theorem for rotating motion is comparable to the translational motion work-energy theorem. It asserts that the net work performed by an external force to spin a rigid body equals the change in rotational kinetic energy of the item.

Explanation

Assume a rigid body rotated via an angle dθ from A to B.

while being influenced by a force F The rigid body is restricted to rotate along a fixed axis that is perpendicular to the page and passes through O when an external force F is applied to point P, whose location is r. Because the rotational axis is fixed, the vector r travels in a circle of radius r, whereas the vector d s is perpendicular to r.

So , The expression is

W = ∫∑F.ds = ∫∑F.(dθ×r)

= ∫dθ.(r ×∑F)

(T = r ×∑F)

W = ∫∑T.dθ

The total work done on a rigid body is the sum of the torques integrated over the angle of rotation.

Hence the expression obtained is W = ∫∑T.dθ

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