**Work done by couple**

Two equal and opposite parallel forces acting on a rigid body at different points constitutes a couple.

Consider a wheel of radius r rotating about its center O. Suppose two unequal forces F act tangentially at points A and B of a diameter of the wheel as shown in the figure. Let θ be the angle of rotation of the wheel. The couple or torque due to the forces are constant.

The work done by each force = force * distance

= F * s

= F * r. θ

Where θ is in radian and distance = AA' = BB' = s = rθ

.: total work done W = F * r. θ + F * r. θ = 2 F r. θ

But torque, τ = F * 2r = 2Fr

So, W = τθ

Therefore, work done by couple is the product of torque and angle of rotation of a rigid body.

For power, according to definition,

P = dW/ dt = d (τθ)/ dt

= τ dθ/ dt

= τω

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