# Angular momentum sliding beam

1. Mar 30, 2013

### tri5

1. The problem statement, all variables and given/known data
A uniform beam with mass M = 156 kg and length L = 2.3 m slides broadside down along the ice at a speed of v0 = 9 m/s. A man of mass 88 kg, who is initially at rest grabs one end of the beam as it goes past and hangs on as the beam and man go spinning down the ice.

Note: You can assume frictionless motion and the moment of inertia for the man about a vertical axis through his center of mass is negliable. Use the coordinate system shown in the picture, with the origin located at the initial position of the man and the z axis pointed out of the plane.
1)
What is the y coordinate of the center of mass of the system before the collision?
2)
What is the magnitude of the angular momentum of the man + beam system about its center of mass just before the collision?
3)
After the collision, what is the moment of inertia of the man + beam system about an axis perpendicular to the ice through the center of mass of the system?
4)
After the collision, at what angular velocity does the system rotate about its center of mass?
5)
After the collision, what is the linear speed of the center of mass of the system?

2. Relevant equations
in attachment

3. The attempt at a solution
see attachment
I am having a problem with question number 3. I don't know how to calculate the moment of inertia of the beam. I have used the formula for the moment of inertia of a rod about the center of mass and then using the parallel axis theorem, but the answer is deemed incorrect by the automated homework system. Should I try to treat the beam as a point particle(so then to calculate its moment of inertia I would use mr^2) or some other shape. I know to treat the man as a point particle when calculating its moment of inertia.

#### Attached Files:

File size:
14.5 KB
Views:
202
• ###### gAfdE2Q3aAgT4bJeT17dARYB.jpg
File size:
34.1 KB
Views:
251
2. Mar 31, 2013

### Sunil Simha

Did you include the moment of inertia of the man? Though it is negligible about an axis passing through him, it is not so when the axis is different ( as in part 3).