Calculating Angular Momentum: Uniform Rod and Point Mass Collision

[avenkat0]

Homework Statement

A uniform rod (M 4.4 kg, L 0.827 m) starts at rest on a frictionless table. A point mass = 0.808 kg hits the rod at a right angle at speed 6.39 m/s. The block strikes the rod at a distance of 0.12 m below the center of mass, and stops. Assume the block does not stick to the rod. Find:

1. vf, the speed of the center of mass of the rod after the collision.

2. Find the energy lost?

Homework Equations

The Attempt at a Solution

Vf of the cm...
i got omega by finding the linear momentum imparted upon the rod by the force of the colliding object and dividing it by the moment of inertia of the rod rotationg about the center of mass...
but now for the V of the cm... if the rod were just rotating it would be zero but the table is frictionless so there is translational motion...
so i used the formula... .5Mblock*Vblock^2=.5Mrod*Vrod^2 + .5iomega^2
and Vrod came out to be wrong...

is there a flaw in my reasoning...? thank you

 

[borgwal]

Vf of the cm...
i got omega by finding the linear momentum imparted upon the rod by the force of the colliding object and dividing it by the moment of inertia of the rod rotationg about the center of mass...

You go wrong right at the first step. if you insist on calculating omega first, you didn't calculate the angular momentum of the colliding object before the collision.

Fortunately for you the question doesn't ask for omega, but only for the cm velocity. That's easy to calculate: use conservation of...(not energy!)