Angular Speed of a ball of clay

[otodaskee]

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 as shown in the figure. The clay collides with the desk 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? (Don't forget to include the mass m after the collision.)

Homework Equations

L = M x V x R
MVR = I(tot) x W
W = (M x V x R ) / I

The Attempt at a Solution

I(tot) = MR^2 + (2/5)MR^2
MR^2 [1+(2/5)] = 7/5MR^2
W = MVR/[(7/5)MR^2]
W = 5V/5R

Is this correct? What are the units?

 

[ehild]

The moment of inertia for a disk is 1/2 MR^2. You used that of a sphere.

When the units are not specified you do not need to give them, you have to solve the problem symbolically.

If you want to check your result, use the SI units, kg for mass, m for length, m/s for velocity. The unit of the angular momentum is then kg m^2 s^-1, the unit of moment of inertia is kgm^2, and the unit of w is 1/s.

ehild