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

Options

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

A

Explanation

Magnitude of radius vector `vec(r )= |vec(r )|= l` constant.
Magnitude of the momentum `vec(p)` of the bob
= `|vec(p)|` = mv = m`omega l` = constant
As angular momentum `vec(L) = vec(r ) xx vec(p)` and the angle between `vec(r ) and vec(p)` is always `90^(@)`.
`|vec(L)| = l cdot m omega l cdot sin 90^(@) = m l^(2) omega` = constant
Also, `vec(r)` is l aways radially outwards and `vec(p)` is tangential. So `vec(L)` is always directed along the axis of rotation. So its direction is also fixed.