Angular Momentum (Ballistic Pendulum w/ mass)

[Cfem]

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

m_b = .012 kg
m_B = 2.3 kg
m_R = 1.3 kg
L = 1.3 m
r = .65m
v_i = ?

-Conservation of Angular momentum:

A_i = A_f
A_i = (m_b)(v_i)(L) = I_T(w) = A_f

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

(1/3)((m_R)(r)² + (m_b + m_B)(L²)

So,

1: w =([m_b * v_i * L)/I_T

-Conservation of Energy

KE = Change in PE
KE = (1/2)(I_T)w₂

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

PE = m_T * g * h

m_T 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 = (m_R * L + (mB + mb)*r)/mT

h = c - c*cos(35)

Equating KE and PE, then solving for w:

w₂ = (m_T * g * h)*2/I_T

So w is the square root of all that mess.

Equating the above equation with 1 and solving for v_i

v_i = (I_T* sqrt{ (m_T * g * h)*2 / I_T }) / ((m_b)(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.

 

[Borek]

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

 

[Cfem]

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

That should say (1/3)(m_R)(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.