SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

τ τ τ τ ( .30b) If the total torque on the rigid body is zero, the total angular momentum of the body does not change with time. Eq. ( . b) gives the condition for the rotationa l equilibrium of the body.

One may raise a question, whether the rotational equilibrium condition [Eq. . (b)] remains valid, if the origin with respect to which the torques are taken is shifted. One can show that if the translational equilibrium condition [Eq.

. (a)] holds for a rigid body, then such a shift of origin does not matter, i.e. the rotational equilibrium condition is independent of the location of the origin about which the torques are taken. Example .

gives a proof of this result in a special case of a couple, i.e. two forces acting on a rigid body in translational equilibrium. The generalisation of this result to n forces is left as an exercise. Eq.

( .30a) and Eq. ( .30b), both, are vector equations. They are equ ivalent to three scalar equations each. Eq.

( .30a) corresponds to F ix