# Angular Velocity of the Cord

1 vote
75 views In this question , I think we have to conserve angular momentum . But for that how can we find final radii.

asked Nov 13, 2016
retagged Nov 29, 2016
Conserve about point of contact of string.
Please elaborate more on your thought process and if applicable the math you did to solve. As it currently stands, this question doesn't show very much effort and might be closed.

## 1 Answer

2 votes

Best answer

I think this is like the sphere or cylinder rolling on a plane. At each instant the sphere/cylinder is effectively rotating about the instantaneous point of contact, even though this point itself is moving. Same here : at each instant the ball on the string is rotating about the instantaneous point of contact. So angular momentum is constant about the contact point.

When the string has moved through an angle of $\theta$, the contact point has also moved through an angle of $\theta$ around the circle of radius $a$. So the string has shortened from $r_0$ by a distance of $a\theta$.

Therefore at any instant $(r_0-a\theta)\omega=r_0\omega_0$.

answered Nov 13, 2016 by (28,746 points)
edited Nov 13, 2016