# Homework Help: Solid Sphere,Impulse

1. May 20, 2012

### ZxcvbnM2000

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

A uniform solid sphere has radius R and mass M. It is initially at rest but is
free to move, floating in space with nothing touching it. It suddenly receives
an impulse J at a tangent to its surface.

As a function of R, M and J, find formulae for:

(a) the linear velocity of the sphere,
(b) its angular velocity around its centre of mass
(c) its total kinetic energy after the impulse.

2. Relevant equations
L=Iω,J=MV,V=ωR

3. The attempt at a solution

a) All particles on the sphere have the same angular velocity and different linear velocities depending on their distance from the centre.

J=ΔP=M(V-u)=MV so V=J/M Whose velocity is this ? ( V=J/M) .Is it the C.o.M ?

b) L=Iω <=> ω=L/I = 5L/(2MR2) But how can i move from here ?

c) well if i knew how to solve b) then c) is an easy one !

2. May 20, 2012

### Staff: Mentor

Good. That's the velocity of the COM.

What's the angular impulse?

3. May 20, 2012

### ZxcvbnM2000

ΔL=IΔω but since it was stationary at first then ΔL=Iω

It seems to be simple but i still can't understand how to relate these two :S

Last edited: May 20, 2012
4. May 20, 2012

### ZxcvbnM2000

Actually no :S

5. May 20, 2012

### Staff: Mentor

Nothing wrong with that, but what is ΔL in terms of J?

6. May 20, 2012

### ZxcvbnM2000

Hmm dL=Iω=J*R=MVR but i realized that V=ωR is not valid , why is that ?

7. May 20, 2012

### Staff: Mentor

The angular impulse is J*R. Now you can solve for ω.

As to whether V = ωR is valid, that depends on what you mean by V. (In any case, you don't need it here.)