How Does a Clay Ball Impact the Rotation Angle of a Rod?

[shannon12]

Homework Statement

A 75kg, 30 cm long rod hangs vertically on a frictionless, horizontal axle that passes through its centre. A 10kg ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very bottom tip of the rod.
To what maximum angle (measured from the vertical) does the rod (with the clay ball attached) rotate?

Homework Equations

The Attempt at a Solution

Not sure where to start on this, apart from calculating the moment of inertia for the rod and for the ball and adding them together to get a total inertia?
From there, I have no clue.

 

[rl.bhat]

Hi Shannon12, welcome to PF.
What is the momentum of of the clay ball? What is the moment of momentum on the rod?
What is the relation between moment of inertia, angular velocity and momentum of momentum?

 

[shannon12]

Hi Shannon12, welcome to PF.
What is the momentum of of the clay ball? What is the moment of momentum on the rod?
What is the relation between moment of inertia, angular velocity and momentum of momentum?

Thank-you! :D
Umm ok so momentum = mv = 0.01 x 2.5 = 0.25 kg m^-1 s^-1 for the clay ball
And the momentum of the rod is I = 1/12 mL^2 = 1/12 (0.075)(0.3^2) = 5.625 E-4

For the second part, I'm not too certain. Í tried checking my book to see if there were any formulas but I couldn't find one..

 

[rl.bhat]

Moment of the mud ball produces the angular momentum in the (rod+ mud ball) sustem.
So mv*L/2 = I*ω. Due to the angular velocity the system acquires kinetic energy. When the system comes to rest KE is converted to PE.
So 1/2*I*ω^2 = mgh = mgL/2(1 - cosθ)
Solve for θ.