Finding the Center of Percussion

[bd2015]

Homework Statement

A rod of mass M and length L rests on a frictionless table and is pivoted on a frictionless nail at one end. A blob of putty of mass m approaches with velocity v from the left and strikes the rod a distance d rom the end as shown, sticking to the rod.

1. Find the angular velocity of the system about the nail after the collision (already done)
2. Is there a value of d for which linear momentum is conserved? If there were such a value, it would be called the center of percussion for the rod for this sort of collision.

Homework Equations

ω final = $\frac{mvd}{(1/3)ML^2 + md^2}$

The Attempt at a Solution

So, I know that linear momentum most be conserved. I don't know how to find the linear momentum of the rod

 

[TSny]

The linear momentum of any object can be calculated as the total mass of the object multiplied by the linear velocity of the center of mass of the object.

 

[bd2015]

The linear momentum of any object can be calculated as the total mass of the object multiplied by the linear velocity of the center of mass of the object.

So then do I just need to set P initial to P final, and solve for d, without having to worry about angular momentum?

 

[TSny]

Essentially, yes. But you'll need to use your result from part 1 which came from conservation of angular momentum. Also, don't forget to include the final linear momentum of the putty.