Physics Problem on Angular Momentum

[utm01]

Homework Statement

A uniform 4.5 kg square solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1 kg raven flying horizontally at 5.0 m/s flies into this gate at its center and bounces back at 2.0 m/s in the opposite direction. What is the angular speed of the gate just after it is struck by the unfortunate event.

Homework Equations

L=mvl and L=Iw

The Attempt at a Solution

First I calculated the momentum for the bird using L=mvl
L = (1.1 kg)(5.0 m/s)(1.5m/2) = 4.125 kg m/s^2

Then the total momentum after it strikes the square
L(total) = raven + the square

I wasn't sure about the moment of interia equation for the square so I used the one a thin rectangular plate axis along edge = Mr^2/3

= (1.1kg)(-2.0 m/s)(1.5m/s) + (4.5 kg)(.75)^2/3(wf) = -1.65 kg m/s^2 + 0.84375(wf)

I equated this to the intial momentum of the bird
4.125 kg m/s^2 = = -1.65 kg m/s^2 + 0.84375(wf)

wf = 6.8 rad/s which is way off

Answer = 1.71 rad/s

I think I'm having trouble as I can't visual the scenario properly...and help would be great!

 

[ehild]

First I calculated the momentum for the bird using L=mvl
L = (1.1 kg)(5.0 m/s)(1.5m/2) = 4.125 kg m/s^2

Then the total momentum after it strikes the square
L(total) = raven + the square

I wasn't sure about the moment of interia equation for the square so I used the one a thin rectangular plate axis along edge = Mr^2/3

= (1.1kg)(-2.0 m/s)(1.5m/s) + (4.5 kg)(.75)^2/3(wf) = -1.65 kg m/s^2 + 0.84375(wf)

Check the data in red.

ehild

 

[gneill]

The moment of inertia of a rectangular plate with dimensions a x b about its center, the axis being perpendicular to the sides of length b is

$\frac{1}{12} M \; b^2$

Note that the full length of the side, 'b' is used. Apply the parallel axis theorem to move the axis of rotation to the edge (along and 'a' side).