Moment of Inertia Ball and Stick Collision

[tachu101]

Homework Statement

A mass is dropped from height (h) onto one end of a stick of mass (m) and of length (l) pivoted around the opposite end. The moment of inertia of the stick is 1/3ML^2. Upon collision the mass adheres to the stick.

a. Find speed of mass just before impact
b. Find angular speed of the system immediately after impact
c. Find linear speed of the mass (m) at its lowest point (when stick is vertical)
d. Determine the mechanical energy lost as a result of the collision.

Homework Equations

Conservation of angular momentum
angular kinematics equations

The Attempt at a Solution

For the first part I think I found easily with vf^2=Vo^2+2ah which will get you vf=(2ah)^1/2
The last three parts I am very confused about. I have that Io wo=If wf The last part I would think I would use the kinetic energy at the start and at the bottom.

 

[djeitnstine]

Remember the relationship between $$\omega$$ and velocity $$v = r \omega$$ also remember in this incident the complete momentum equation entails linear momentum so

$$mv_{i} + I \omega_{i} = mv_{f} + I \omega_{f}$$

remember there is no initial rotational momentum

I am a tad rusty right now since its been over 2 months since I've last seen this stuff (vacation lol)

I know for sure this model holds for conservation of energy though

comment on and/or let me know how it works out

Edit: remember your $$v_{f}$$ (from kinematics) = $$v_{i}$$ (in the momentum equation)

 

[tachu101]

Does Mo*Vo= I*Wfinal and then is I=(1/3)(2M)(L^2) this will cause the angular speed to be really complicated looking (3/2L^2)*(2gh)^(1/2) and is no mechanical energy lost in the system?

 

[Veszafein]

I know for sure this model holds for conservation of energy though

Also, I am having trouble finding the equation for linear motion compared to rotational, does anyone have a link to the trig equation?

 

[Veszafein]

v = rw
linear velocity = radius x angular speed

 

[Doc Al]

Does Mo*Vo= I*Wfinal and then is I=(1/3)(2M)(L^2) this will cause the angular speed to be really complicated looking (3/2L^2)*(2gh)^(1/2) and is no mechanical energy lost in the system?

What's the angular momentum of the system before the collision?
What's the rotational inertia of the system once the ball attaches to the stick?
Use this to find the rotational speed just after the collision.

What's the energy of the system just before the collision? Just after the collision?