Question

A stone is attached to a string and is revolved in a circular path with constant angular velocity in the
ste its angular momentum is L. If the length of the string is reduced to half and again it is revolved
with the same angular velocity o then find its angular momentum.
al dir quienended from one of its onds and is rotated at the rate​

Answer 1

That what I could do..

Let m=mass of the stone

ω= angular velocity

r=the radius of the circular path or length of the string...

L' is the final angular momentum.

Answer 2

angular momentum would be 1/4th of its initial value.

angular momentum is the cross product of seperation from fixed point to point of observation and linear momentum.

i.e., L = r × P = r × mv = m(r × v)

when velocity is perpendicular to point of observation, r

then, L = mvr

as stone is rolling with an angular velocity, ω in a circular path of radius r.

then, v = ωr

so, L = mωr²

if m and ω are constant then, L ∝ r²

i.e., angular momentum is directly proportional to square of point of observation.

here length of string is reduced to half.

so, L/L' = (r/r/2)² = 4

⇒ L' = L/4

hence, angular momentum would be 1/4th of its initial value.

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