How Is Angular Speed Calculated After Clay Impacts a Wheel?

[mrshappy0]

Homework Statement

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.

Homework Equations

T=rF=Iα.

The Attempt at a Solution

I don't have a textbook 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]

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

 

[mrshappy0]

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

 

[mrshappy0]

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

 

[Doc Al]

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]

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

 

[Doc Al]

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]

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

 

[Doc Al]

Which is d in this problem.

Ah, yes it is.