# Angular momentum of spinning mass on wheel

1. Apr 25, 2013

### elemis

1. The problem statement, all variables and given/known data

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?

2. Relevant equations
v=wr
L=Iw

3. 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 ?

2. Apr 25, 2013

### TSny

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

3. Apr 25, 2013

### elemis

Yes, is that a problem ?

4. Apr 25, 2013

### TSny

Did you square the velocity when finding the initial angular momentum? Why should it be squared in the final angular momentum?

5. Apr 25, 2013

### elemis

Ooops !!! I have absolutely no idea where that came in from. YIKES !

So final tangential velocity is 2, correct ?

6. Apr 25, 2013