Conservation of Angular Momentum

For translational motion we had and for  we had  = constant, i.e. conservation of momentum. Similarly from , then if there are no external torques  then the total angular momentum is conserved, namely

Example A student is spinning on a stool and holding two heavy weights with outstretched hands. If the student brings the weights closer inward, show that the spin rate increases.

Solution For a rigid body spinning about a fixed axis we had . Angular momentum is conserved, thus

or

The moment of inertia of the two weights is I = 2Mr² where r is the length of the student's arm. The rotational inertia of the student remains the same. Thus

giving

And r_i > r_f giving .

 MASTER TABLE