M-Rot 2: Conservation of angular momentum

PIRA: 1Q20.10

Equipment: stand rod with spike in top, rubber stopper tied to the end of a cord attached to the spike; two masses on a horizontal slide, appropriately mounted cords and pulleys so that these masses can be pulled in toward the center as the system rotates. The two masses on horizontal slide are in Set 8, Cabinet 2, Shelf 2 and the stand rod with spike is between Rooms 3 and 5.

Procedure: This pair of experiments is designed to show the difference between conservation of momentum and conservation of angular momentum. If the rubber stopper is pulled out from the stand rod till the cord makes an angle of about 30 with the vertical and started in a horizontal circular path (a conical pendulum), the cord will wind up on the rod and decrease the radius of the circle of revolution. However, since the instantaneous velocity is always at right angles to the direction of the cord, there can be no linear acceleration of the stopper. The magnitude of linear momentum is conserved except for the slight conversion of gravitational potential energy to kinetic energy as the center of mass of the stopper is lowered by the decrease of the swing.

In the apparatus with the two masses on a horizontal slide the arms are set rotating with the masses at the outer extremities. Then the cords are pulled upward and the masses move toward the center with an ever increasing rate of rotation (and velocity magnitude, as a matter of fact). In this case angular momentum is conserved since the force the cords exert on the masses passes through the constant axis of rotation and there is no external torque. Kinetic energy does increase in this process since the force applied by the cords is not perpendicular to the instantaneous velocity in this case.