Question

A mass is whirled in a circular path with constant angular velocity and it's angular momentum is l. If the string is now halved keeping the angular velocity the same, the angular momentum is

Answer 1

L/4

Acc. to formula L = mvr = mωr2

Keeping ω constant, if, r is halved, the L will get one-forth

Answer 2

The angular momentum becomes one-fourth.

We know, angular momentum l is given as:

l = mr²ω

r is the radius and ω is the angular velocity.

Given that ω is kept constant and m, the mass is a constant itself. So,

l ∝ r²

When the string is halved its new 'r' is r' = r/2

So, angular momentum(l') ∝ (r/2)²

or, it is proportional to r²/4

(l'/l) = ( r²/4 /1) = 1/4

So, it becomes one-fourth.