# Express the angular velocity

1. Jun 18, 2012

### Jalo

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

A mass m1 with speed v1i colides with a mass m2 of length 1m, initially at rest, and gets stuck with it.
(a) Express the angular velocity in functon of v1i. (m=m1=m2)

2. Relevant equations

w=v/r

3. The attempt at a solution

Since the collision is totally inelastic I can say
m1*vi1=(m1+m2)vf
Since all masses are equal I can say
vi1=2vf⇔vf=v1i/2
Since w=v/r
w=vf/r⇔w=0.5*v1i/0.5⇔w=v1i

This is wrong for some reason... Can anyone lead me in the correct way?

Thanks.
D.

2. Jun 18, 2012

### JtValentine

If the length of the bar is 1, then the radius of a circle that the bar makes as it rotates 360 degrees means r=1. Thus w= 0.5V1i/1 = V1i/2.

3. Jun 18, 2012

### Staff: Mentor

I don't quite understand the diagram. What's that ball like thing on top of m2? Is m2 fixed at some point?

4. Jun 18, 2012

### JtValentine

Doc Al has a great point. More explanation is needed. I just assumed the ball at the top of the bar was an axis of rotation, but I could be wrong.

5. Jun 18, 2012

### Jalo

It doesn't say nothing about the ball, so I'm pretty sure it's the axis of rotation

6. Jun 18, 2012

### Staff: Mentor

Assuming that m2 is constrained to rotate about that axis, you cannot apply conservation of linear momentum. (The axis will exert forces on m2.)

But what other quantity is conserved?

7. Jun 18, 2012

### Jalo

Angular momentum?

8. Jun 18, 2012

Right!