Question

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed $ \omega$. If the angular momentum of the system, calculated about O and P are denoted by $ L_o$ and $ L_p $ respectively, then

• A. $ L_0$ and $L_p$ do not vary with time
• B. $ L_0$ varies with time while $L_p$ remains constan
• C. $ L_0$ remains constant while $L_ P$ varies with time
• D. $L_0$ and $L_P$ both vary with time

Answer 1

Answer: (C)

Angular momentum of a particle about a point is given by $L = r \times P = m(r \times v )$
For $L_0$
$ | L |= (mvrsin \theta ) = m (R \omega ) (R )sin 90^\circ $ = constant
Direction of $ L_0 $ is always upwards. Therefore, complete $ L_0 $ is constant, both in magnitude as well as direction.
For $L_p$
$|L _P |= (mvrsin \theta ) = (m) (R \omega) (l)sin 90^ \circ = (mRl \omega)) $
Magnitude o f $L_P$ will remain constant but direction o f $L_P$ keeps on changing.