# Common angular velocity

1. Dec 10, 2013

### KiNGGeexD

This is more a question of understanding than physics:)

I have two rotating wheels each with a given radius and a given mass, if one is rotating with an angular velocity and the other is stationary and the stationary one is brought into contact with the rotating one what is the common angular velocity? Ohhh also I didn't mention it is probably obvious but they are on a common x and y plane:)

So the first thing I noticed was that angular momentum is conserved in the system! So using the given mass and radius and angular velocity I calculated an angular momentum (before)

And I used this momentum to calculate the angular velocity of the second one?

But my question is how do I get the "common" angular velocity!

Because when I use the above method the angular velocity of the second one comes out to be larger than the first which is understandable because it has a smaller mass hence smaller inertia but I am not sure I know how to obtain a common velocity?

Any help would be great thank you:)

2. Dec 10, 2013

### voko

They will not necessarily have the same angular velocity. However, at the point of their contact they will have... what linear velocity?

3. Dec 10, 2013

### KiNGGeexD

Well yea if they have angular velocity they have tangential velocity don't they?
But I don't see how the linear velocity is related to calculating the common angular velocity

4. Dec 10, 2013

### voko

What is the relationship between tangential (linear) and angular velocity of a wheel?

5. Dec 10, 2013

### KiNGGeexD

Well v=rω

So ω=v/r :)

6. Dec 10, 2013

### voko

7. Dec 10, 2013

### KiNGGeexD

Form my method in the original question I would have

v(1)=5.236
v(2)=13.09

would linear velocity still be in m/s?

But those are the respective linear velocities

8. Dec 10, 2013

### voko

So imagine two wheels in contact with each other. Going at different linear velocities. What would happen next?