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## Homework Statement

A uniform rod of length L rests on a frictionless horizontal surface. The rod pivots about a fixed frictionless axis at one end. The rod is initially at rest. A bullet traveling parallel to the horizontal surface and perpendicular to the rod with speed v strikes the rod at its center and becomes embedded in it. The mass of the bullet is one-fourth the mass of the rod.

Mass(bullet) = (1/4)Mass(rod)

__A)What is the final angular speed of the rod?__

__B)What is the ratio of the kinetic energy of the system after the collision to the kinetic energy of the bullet before the collision?__

## Homework Equations

v = ω*L

KE = (1/2)Iω

^{2}

## The Attempt at a Solution

I know that v = ω*L is correct. I am missing the coefficient in front of it. The only thing that I can think of is the fact that the mass of the bullet being 1/4 that of the rod will somehow be put into this equation as well as the equation for part B.

**So for part A...**

I am not sure of any equation that will get me the proper coefficient for the answer of ω = v/L

**For part B...**

__Bullet__

KE = (1/2)Iω

^{2}

KE = (1/6)mL

^{2}ω

^{2}

KE = (1/6)mv

^{2}

__System__

KE = (1/2)Iω

^{2}

KE = (1/6)mL

^{2}ω

^{2}

.....since mass of the bullet is 1/4 of the system....

KE = (1/24)mL

^{2}ω

^{2}

KE = (1/24)mv

^{2}

When we put {KE = (1/24)mv

^{2}}/{KE = (1/6)mv

^{2}}

1/4

But that is wrong as well...