# Homework Help: Angular velocity when mass is added at center of rotation

1. Nov 30, 2013

### wootman23

1. The problem statement, all variables and given/known data
A guy is spinning on a chair with his hands at rest on his lap. As he is spinning, a large mass drops into his hands/lap. Does the guy continue spinning at the same rate, a slower rate, or a faster rate?
This video demonstrates what happens when the guy drops mass:
http://media.pearsoncmg.com/aw/aw_0media_physics/vtd/video20.html

Please do not answer the question for me, but help me understand the problem and relevant equations.

2. Relevant equations
L = Iω = m(r^2)ω -----I think this this is the equation I need....

3. The attempt at a solution
If mass is added, shouldn't ω decrease due to the conservation of angular momentum?
But I did a quick experiment with my brother and I didn't seem to slow down...

2. Nov 30, 2013

### haruspex

Angular momentum is not just a question of moving mass - the mass has to have some angular inertia (moment of inertia) to be interesting. Yes, if the mass is not already spinning, when dropped into your lap it will slow your spin, but it might not be that obvious. If the mass is narrow (a small heavy lump, or a tall pole) and drops into your lap at your axis of spin then it will have very little moment of inertia about that axis, so won't require much angular momentum to bring it up to your spin rate.
Dropping mass, as in the video, is rather different. The bags did not drop straight down; each flew off tangentially. This means they still had angular momentum about his axis. So in this case it does not matter how much moment the bags had about the axis, his spin rate will not change.

3. Nov 30, 2013

### wootman23

Ohhh so since the long, heavy bean bag isn't spinning as its dropped onto the guy's lap, it will will require some angular inertia to get it to spin...and to do this, it "steals" some angular speed from the guy which causes him to slow down? Do I have that right?

4. Nov 30, 2013

### wootman23

Ohhh so since the long, heavy bean bag isn't spinning as its dropped onto the guy's lap, it will will require some angular inertia to get it to spin...and to do this, it "steals" some angular speed from the guy which causes him to slow down? Do I have that right?

5. Nov 30, 2013

### haruspex

Yes.

6. Nov 30, 2013

### wootman23

Yup, you were right! Thank you for the explanation and confirmation!