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 mrshappy0 Nov13-11 05:26 PM

Angular Velocity Of A Wheel

1. The problem statement, all variables and given/known data
A wad of sticky clay with mass 2.45 kg and velocity vi = 52.0 m/s is fired at a wheel of moment of inertia 1.2 kg m2 and radius R = 1.26 m. The wheel is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at distance d = 0.842 m from the center.
Find the angular speed of the cylinder (in rad/s) just after the clay strikes and sticks to the surface of the wheel.

2. Relevant equations

T=rF=Iα.

3. The attempt at a solution
I don't have a text book with me so I am trying to work through this by searching the internet and my memory. I am thinking in order to solve this you would just take the angular force times the radius and you would have torque. Then from there you would find the angular speed from the torque but I don't see how you would find the torque if the problem only gives you the velocity of the clay projectile.

 Doc Al Nov13-11 05:32 PM

Re: Angular Velocity Of A Wheel

Since you don't have information of the forces involved, see if you can apply a conservation law to solve the problem.

 mrshappy0 Nov13-11 05:38 PM

Re: Angular Velocity Of A Wheel

Right as I finished typing I thought of conservation of momentum but isn't the clay piece an external force?

 mrshappy0 Nov13-11 05:39 PM

Re: Angular Velocity Of A Wheel

Meaning the momentum is not conserved from the initial state of the wheel to the final state.

 Doc Al Nov13-11 05:41 PM

Re: Angular Velocity Of A Wheel

Quote:
 Quote by mrshappy0 (Post 3614250) Right as I finished typing I thought of conservation of momentum but isn't the clay piece an external force?
While the momentum of either one--clay piece or wheel--isn't conserved by itself, the momentum of the system (the angular momentum) is.

 mrshappy0 Nov13-11 05:46 PM

Re: Angular Velocity Of A Wheel

Oh okay! So does would the initial momentum of the clay equal mvd?

 Doc Al Nov13-11 06:03 PM

Re: Angular Velocity Of A Wheel

Quote:
 Quote by mrshappy0 (Post 3614263) So does would the initial momentum of the clay equal mvd?
No. You must use the distance between the line of motion of the clay and the axis of rotation.

 mrshappy0 Nov13-11 06:17 PM

Re: Angular Velocity Of A Wheel

Which is d in this problem. Thanks for you help.

 Doc Al Nov13-11 06:21 PM

Re: Angular Velocity Of A Wheel

Quote:
 Quote by mrshappy0 (Post 3614311) Which is d in this problem.
Ah, yes it is. :wink:

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