# Angular velocity uniform rod problem

Poutine
Hi all, recently joined and having abit of trouble with a problem (several actually but I managed to figure out how to get started on one of them).

In any case the problem says:
Four thin, uniform rods each of mass M and length d = .75 m, are rigidly connected to a vertical axle to form a turnstile. The turnstile rotates clockwise about the axle, which is attached to a floor, with initial angular velocity w = -2.0 rad/s. A mud ball of mass m = M/4 and inital speed vi = 15 m/s is thrown and sticks to the end of one rod at an angle 60 degrees. Find the final angular velocity of the ball-turnstile system.

Now I think I have to use the Conservation of Angular momentum. As such I need to find the inertia of the turnstile which I think turns out to be IT=(4/3)*M*d^2

I think the formula I'm going end up with will probably be
It * wf + Ib * wf = IT* wi + angular momentum of the ball before the contact

The thing is I don't know how to get further from here.

Tom Mattson
Staff Emeritus
Gold Member
I don't have a table of rotational inertias for different shapes in front of me, so I won't comment on that until tomorrow, after I look it up.

But as for where you go after that, you're basically done. You will have something like:

Ii&omega;i=If&omega;f

You know everything except &omega;f
(Don't forget to treat the mudball as a point mass, so Imud=mr2.)

Poutine
Okay you answered my main question which is what is Imud? But I don't understand why that is true. Why is it mr^2, I was thinking it might have been 2/5 mr^2 but it seems I was wrong but I don't understand why.

Just to be certain the angular momentum before contact would be (M/4)*v*d*cos 60 right?

Tom Mattson
Staff Emeritus