Angular momentum of spinning mass on wheel

[elemis]

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?

Homework Equations

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=2^0.5

Is this correct ?

 

[TSny]

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

 

[elemis]

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

Yes, is that a problem ?

 

[TSny]

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

 

[elemis]

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]

Yes, that's the correct answer.