What is the Angular Velocity of a Sliding Beam and Man System?

[BIOPSYCH]

Homework Statement

A 230 kg beam 2.7 m in length slides broadside down the ice with a speed of 18 m/s. A 65 kg man at rest grabs one end as it goes past and hangs on as both he and the beam go spinning down the ice. Assume frictionless motion.

(a) How fast does the center of mass of the system move after the collision?

(b) With what angular velocity does the system rotate about its center of mass?

Homework Equations

For part (a)

(mass before)(linear velocity) = (mass after)(linear velocity after)

velocity at CM: 1/2(linear velocity after)

For part (b):

v = [tex]\omega[/tex]r

The Attempt at a Solution

Part (a):

230(18) = (230+65)v

v= 14.03 m/s

v at CM: 1/2(v)

v at CM: 7.02 m/s

Part (b):

v=[tex]\omega[/tex]r

14.03 = 2.7 [tex]\omega[/tex]

[tex]\omega[/tex]= 5.2 rad/s

Is this correct? Is there something I am missing?

 

[BIOPSYCH]

Does anyone know if this approach is correct?

 

[BIOPSYCH]

Does anyone know if this is correct?