Constrained motion question (using moments of inertia/energy)

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SUMMARY

The discussion centers on a constrained motion problem involving moments of inertia and energy calculations for a system comprising a disc, an arm, and a collar. The user calculated the initial potential energy for the disc, arm, and collar, arriving at values of 41.62 joules and 20.81 joules for the arm and collar, respectively. However, upon calculating the final speed of the collar, the user obtained 1.04 m/s, while the expected answer is 7.315 m/s. The primary issue identified is likely related to the kinetic energy term of the arm, which requires further clarification.

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Mutant_Fruit
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I've attached a screenshot of the question. This is what I've tried so far:

I've calculated the initial energy of the system (which is all potential energy):
Energy of disc:
0.5*I*w^2 + 0.5 *m*v^2 + m*g*h
= 0 + 0 + 0

Energy of arm:
0.5*m*v^2 + m*g*h
= 0 + 4*9.81*1.5Cos(45)
= 41.62 joules

Energy of collar:
0.5*m*v^2 + m*g*h
= 0 + 1*9.81*3Cos(45)
= 20.81 joules

Then i moved time on until the supporting arm BC was horizontal and calculated the energy at that stage (which would be all kinetic). When i do that, i end up calculating that the speed of the collar is 1.04 m/s. However, the answer is supposed to be 7.315 m/s.

I'm doing something wrong, but i can't figure out what it is. Any hints on how this is supposed to be solved would be great.

Thanks.

http://img127.imageshack.us/img127/3230/question8wo.th.jpg
 
Last edited by a moderator:
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In all probability, your flaw lies in determining the kinetic energy term of the arm. Specify what you did.
 

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