Question

A small ball of mass m suspended from the ceiling at a point O by a thread of length l moves along a horizontal circle with a constant angular velocity ω. Relative to which points does the angular momentum M of the ball remain constant? Find the magnitude of the increment of the vector of the ball's angular momentum relative to the point O picked up during half a revolution.

Answer 1

(a) The ball is under the influence of forces vector T and m vector g at all the moments of time, while moving along a horizontal circle. Obviously the vertical component of vector T balance m vector g so the net moment of these two about any point becoems zero. The horizontal component of vector T which provides the centripetal acceleration to ball is already directed toward the centre (C) of the horizontal circle, thus its moment about the point C equals zero at all the moments of time. Hence the net moment of the force acting on the ball about point C equals zero and that’s why the angular momentum of the ball is conserved about the horizontal circle.