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 withan angular speed omega rad/s about the vertical support. About the point of suspension

A bob of mass m attached to an inextensible string of length l is susp

1.	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 withan angular speed omega rad/s about the vertical support. About the point of suspension
Answer» ANGULAR momentum is conserved angular momentum changes in magnitude but not in direction angular momentum changes in direction but not in magnitude angular momentum changes both in direction and magnitude Solution :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.