IIT (NTSE/Olympiad)  

Circular Motion & Rotational Dynamics

12. Forces Couple

12. Forces Couple

(a) When two forces of equal magnitude act on different points and in opposite direction, these force form a couple.
(b) The effect of couple is known by its moment.
(c) The moment of couple is equal to the product of magnitude of any force and perpendicular distance between the force.
Moment of couple = (F) (r)
(d) The couple causes the rotational motion in the body.
(e) Generally both couple and torque carry equal meanings.
When there is only one force applying on a body the reaction force forms torque with it.
(f) The work done by couple on a body is equal to work done by torque
∴ Work done by couple = work done by torque =
(g) If particle complete n rotations under the effect of couple or torque, work done W = τ (2 π n)
(h) As on stretching a spring energy is stored in it, in the same way as on twisting a wire the work done by torque is stored in the form of energy.

τ = C θ ¼Restoring torque½, (where C = twisting coefficient)

IIT (Class X)