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

AI Thread Summary
The discussion focuses on calculating the center of mass velocity and angular velocity of a system consisting of a sliding beam and a man who grabs it. For part (a), the center of mass velocity is determined to be 7.02 m/s after applying conservation of momentum, leading to a post-collision speed of 14.03 m/s. In part (b), the angular velocity is calculated using the relationship between linear velocity and radius, resulting in an angular velocity of 5.2 rad/s. Participants seek confirmation on the correctness of these calculations and the methodology used. The approach appears sound based on the provided equations and results.
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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 = \omegar

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=\omegar

14.03 = 2.7 \omega

\omega= 5.2 rad/s

Is this correct? Is there something I am missing?
 
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Does anyone know if this approach is correct?
 
Does anyone know if this is correct?
 
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