Work done by Couple | Physics Grade XI Rotational Dynamics Reference Note

work done

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Work done by Couple | Physics Grade XI Rotational Dynamics Reference Note

Work done by Couple

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

Work done by coupleConsider 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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