How Does Angular Momentum Affect Projectile and Rod System Post-Collision?

AI Thread Summary
The discussion focuses on a physics problem involving a projectile colliding with a stationary rod, requiring calculations of angular speed and fractional mechanical energy loss after the collision. The equations of motion and energy conservation principles are applied, specifically using angular momentum conservation to find the angular speed immediately post-collision. A common mistake noted is in calculating the fractional loss of mechanical energy; the final energy loss must be divided by the initial kinetic energy of the projectile. Clarification is provided that the correct approach for part (b) involves this division to determine the fractional loss accurately. The conversation emphasizes the importance of understanding energy concepts in collision scenarios.
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Homework Statement


A projectile of mass m moves to the right with a speed vi. The projectile strikes and sticks to the end of a stationary rod of mass M, of length d, that is pivoted about a frictionless axle through its center.

p11-54.gif


(a) Find the angular speed of the system right after the collision. (Use v_i for vi, m, M, and d as appropriate in your equation.)
(b) Determine the fractional loss in mechanical energy due to the collision. (Use v_i for vi, m, M, and d as appropriate in your equation.)

Homework Equations



If\omegaf=Ii\omegai
W= K1-K2

The Attempt at a Solution


http://qaboard.cramster.com/Answer-Board/Image/2007111219463329548144409250092.jpg
i did it like this but for some reason my part (b) is saying that I'm wrong. Can someone help?
 

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It all looks fine, but question (b) asks about the *fractional* energy loss, so you should divide your final answer by mv^2/2.
 

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