Improve Your Test Review: Solving for Final Angular Speed with a Spinning Mass

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To solve the problem of finding the final angular speed of a mass connected to a cord, the principle of conservation of angular momentum is applied. The initial parameters include a mass of 1.32 kg, a cord length of 1.62 meters, and an initial angular speed of 8.0 radians per second. When the cord is pulled inward to 0.33 times its original length, the relationship r1^2*v1 = r2^2*v2 is used to determine the final angular speed. The calculations suggest that the final angular speed is 73.46 radians per second. This approach effectively demonstrates the conservation of angular momentum in a rotating system.
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im stuck on one of the homework problems I am reviewing for a test. any help would be appreciated. I am not sure on how to set up the problem.

a small 1.32 kg mass is connected to a cord of length 1.62 meters, and spun at a constant angular speed of 8.0 radians per second. if the cord is pulled inward so that the mass is only 0.33 times as far from the axis as it started out, what is the final angular speed of the mass at its new distance from the axis?
 
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HINT: Conservation of angular momentum
 
thats what i was thinking.. so i would set them equal.. what would the moment of inertia be for this case?
 
Since the mass is small, I = mr^2, where r is the length of the cord.
 
oh ok. i got it

since the mass would cancel out i got r1^2*v1=r2^2*v2 with the answer 73.46radians per second.

is that correct?
 

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