Question

what do you understand by angular momentum of a partical? derive a relation between angular momentum of the particle and torque acting on it.

Answer 1

Here is one derivation which I have received in argument to my work:

“angular momentum = moment of inertia x angular velocity

or L = I x w where for a lumped mass m on a lever arm r,

I = r^2 x m, and w = v/r where v is the tangential velocity of the rotating mass m. I use w instead of omega because my keyboard has no greek.

then we have angular momentum L = rmv.

If L changes in time, we have

dL/dt = d/dt(I x w) = I x d/dt(w)

where the time derivative of w is alpha, the angular acceleration. So

dL/dt = I x (alpha)

I is rotational mass, alpha is rotational acceleration, and since force = mass x acceleration we have

torque T = I x (alpha), newton's law for rotating systems.

If we do not apply any torque to the system, thenalpha is zero, which means

dL/dt = 0 which means

ANGULAR MOMENTUM IS CONSTANT IN THE ABSENCE OF TORQUES.”

Note that this derivation is correct if and only if one assumes that the radius remains constant. Angular momentum is defined as L=r x p, so when the radius changes angular momentum will change. Angular momentum is not conserved. It appears to be conserved when the radius remains constant because the momentum is conserved.