Question

A bob of mass m attached to an inextensible string of length / is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical support. About the point of suspension,

(a) angular momentum is conserved

(b) angular momentum changes in magnitude but not in direction

(c) angular momentum changes in direction but not in magnitude

(d) angular momentum changes both in direction and magnitude

Answer 1

Correct option (c) angular momentum changes in direction but
not in magnitude
Explanation :

Angular momentum of the pendulum about the suspension point o is

Then, v can be resolved into two components, radial component v_rad and axial component v_axial. Due to v_rad , will be axial and due to v_axial , L will be radially outwards as shown.

So, net angular momentum will be as shown in figure whose value will be constant ( |L| = mv) But its direction will change as shown in the figure.

L = m (r x v)

where, r = position vector of particle point O.