# Angular Momentum (Ballistic Pendulum w/ mass)

I only have one more attempt on this question before I lost all of the points, so detailed help would be much appreciated. I understand everything conceptually (I think), but I don't know where I went wrong.

## Homework Statement

A 2.3 kg wood block hangs from the bottom of a 1.3 kg, 1.3 meter long rod. The block and rod form a pendulum that swings on a frictionless pivot at the top end of the rod. A 12 g bullet is fired into the block, where it sticks, causing the pendulum to swing out to a 35 degree angle.

## Homework Equations

Conservation of angular momentum
Conservation of energy
Moment of Inertia

## The Attempt at a Solution

mb = .012 kg
mB = 2.3 kg
mR = 1.3 kg
L = 1.3 m
r = .65m
vi = ?

-Conservation of Angular momentum:

Ai = Af
Ai = (mb)(vi)(L) = IT(w) = Af

Where w is the final angular velocity
Where IT is the total moment of inertia of the system. Given by:

(1/3)((mR)(r)2 + (mb + mB)(L2)

So,

1: w =([mb * vi * L)/IT

-Conservation of Energy

KE = Change in PE
KE = (1/2)(IT)w2

Change in PE, treating initial position of the pendulum as PE = 0:

PE = mT * g * h

mT is the sum of the masses
Where h is the change in height, denoted by the change in the center of mass as the pendulum rotates:

center of mass = c = (mR * L + (mB + mb)*r)/mT

h = c - c*cos(35)

Equating KE and PE, then solving for w:

w2 = (mT * g * h)*2/IT

So w is the square root of all that mess.

Equating the above equation with 1 and solving for vi

vi = (IT* sqrt{ (mT * g * h)*2 / IT }) / ((mb)(L))

Which gives me something like 441. I'm really frustrated with this and I'm not sure what I did wrong. Thanks in advance.

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Borek
Mentor
I don't get how you calculated total moment of inertia.

That might have been one of those "two o'clock in the morning typos".

That should say (1/3)(mR)(L2) + that second half. Formula of a rod rotated about an end summed with the moment of inertia of the bullet and block, treated as a point.

Beyond that, is there any other mistakes? Thanks for catching that.