# Angular momentum of spinning mass on wheel

## Homework Statement

An object of mass 2 kg is held in circular motion by a string of negligible mass.
Initially the radius is 1 m and the tangential velocity is 4 m/s. The string is
subsequently let out gradually until the radius doubles to 2 m. There are no
frictional or resistive forces present. What is the final tangential velocity?

v=wr
L=Iw

## The Attempt at a Solution

Initially the angular momentum is : 2*12*$\frac{4}{1}$ = L = 8

By conservation of angular momentum we should have L = 8 when the string becomes 2m long :

2*22*$\frac{v^2}{2}$ = 8 v=20.5

Is this correct ?

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TSny
Homework Helper
Gold Member
In your equation for the final angular momentum, you squared the velocity. Is that correct?

In your equation for the final angular momentum, you squared the velocity. Is that correct?
Yes, is that a problem ?

TSny
Homework Helper
Gold Member
Did you square the velocity when finding the initial angular momentum? Why should it be squared in the final angular momentum?

Did you square the velocity when finding the initial angular momentum? Why should it be squared in the final angular momentum?
Ooops !!! I have absolutely no idea where that came in from. YIKES !

So final tangential velocity is 2, correct ?

TSny
Homework Helper
Gold Member