Solving for Final Angular Speed of Clay & Disk

[lobbob]

Homework Statement

A ball of clay of mass m travels with velocity v in a path tangent to a disk of radius R and mass M. The clay collides with the disk tangentially to its outer rim (a totally inelastic collision) and the clay and disk begin to spin about the axis.

What is the final angular speed of the clay and disk?

Homework Equations

I don't know any?

The Attempt at a Solution

I found some random equations which I tried using. m*v+M*v2*cos (theta) = (m+M) * vf*cos (theta)f. And M*v2*sin (theta)= (m+M)*vf*sin (theta)f. I just plugged in the values but I got weird answers. I got mv/(m+M)*vf*cos(theta)f. I also got 0=vf * sin (theta)f. Then I took the arcsin for the second equation and got (theta)f=0. So I ended up with mv/(m+M)=vf

I would just like somebody to show me a step by step solution and the correct equations to use. Any help appreciated though!

 

[ehild]

It is very silly to use random equations, without knowing what they mean. What are v, C, m, M, theta and f in the equation you picked up? What is the situation they are applied? Is there any R and angular speed in them?

ehild

 

[paisiello2]

Instead of trying a random equation maybe try and apply the principles of conservation of energy?

 

[lobbob]

Instead of trying a random equation maybe try and apply the principles of conservation of energy?

Do you mean principles of conservation of angular momentum or energy. Also, could you start me off. I get confused with the equations. Or since this looks like a inelastic collision in two dimensions is there any handy formula? Thanks!

 

[lobbob]

It is very silly to use random equations, without knowing what they mean. What are v, C, m, M, theta and f in the equation you picked up? What is the situation they are applied? Is there any R and angular speed in them?

ehild

By random equations I meant equations that I never used before, but seemed they might work. v is velocity, m is mass of clay, M is mass of sphere, theta is initial angle launched at, and f just means final. So (theta)f meant final angle. I don't think there was any C. So the main reason why the problem confuses me is that they don't give any values really. They just give the variables. The only thing they actually give is theta which is 90deg since it is tangent. So I think the point is to make a general equation or something. You can take the angular velocity as V and the radius is just r for the sphere. The clay is considered a point with mass. Any help appreciated! Also, this looks like a inelastic collision in two dimensions, but I don't know if this helps. Is there any handy formula that could work?

 

[paisiello2]

Do you mean principles of conservation of angular momentum or energy. Also, could you start me off. I get confused with the equations. Or since this looks like a inelastic collision in two dimensions is there any handy formula? Thanks!

Good question! I guess since the collision is inelastic then energy is not conserved. So we should use conservation of angular momentum!

 

[ehild]

By random equations I meant equations that I never used before, but seemed they might work. v is velocity, m is mass of clay, M is mass of sphere, theta is initial angle launched at,

angle with respect to what?

and f just means final. So (theta)f meant final angle. I don't think there was any C. So the main reason why the problem confuses me is that they don't give any values really. They just give the variables. The only thing they actually give is theta which is 90deg since it is tangent. So I think the point is to make a general equation or something. You can take the angular velocity as V

No, angular velocity is denoted by ω.

The collision happens between the piece of clay and a disk, and the disk can rotate about an axis. It does not travel. But the clay and the disk will rotate with common angular velocity ω.

Think what is conserved during the interaction between the clay and the disk. It is inelastic collision. Is energy conserved?
The disk can only rotate about a fixed axis. The axis exerts force on the disk. Is momentum of the clay-disk system conserved?

There is no external torque. So the angular momentum is conserved.
What is the angular momentum of the clay with respect to the axis of the disk? What is the angular momentum of the disk, with the clay stuck at the rim?

You need the equations for angular momentum.

ehild