If `vec(tau)xxvec(L)=0` for a rigid body, where `vec(tau)=` resultant torque & `vec(L)` =angular momentum about a point and both are non-zero. Then

The correct relation between torwue tau and angular momentum L is

Torque (vec tau) acting on a rigid body is defined as vec tau = vec A xx vec L , where vec A is a constant vector and vec L is angular momentum of the body. The magnitude of the angular momentum of the body remains same. vec tau is perpendicular to vec L and hence torque does not deliver any power to the body.

The torque vec tau on a body about a given point is found to be equal to vec A xx vec L where vec A is a constant vector and vec L is the angular momentum of the body about the point. From this its follows that -

Obtain tau=Ialpha from angular momentum of rigid body.

If L is the angular momentum and tau is the torque then prove that ( tau = dL/dt)

The relation between the torque tau and angular momentum L of a body of moment of inertia I rotating with angular velocity omega is

The torque tau on a body about a given point is found to be equal to AxxL where A is a constant vector, and L is the angular momentum of the body about that point. From this it follows that

Two particle are initially moving with angular momentum vec(L)_(1) and vec(L)_(2) in a region of space with no external torque. A constant external torque vec( tau) then acts on one particle, but not on the other particle, for a time interval Delta t . What is the chargne in the total angular momentum of the two particles ?