# Common angular velocity

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:)

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

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

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

Well v=rω

So ω=v/r :)

Form my method in the original question I would have

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