Amount of energy lost to friction due to change in rotational inertia

AI Thread Summary
The discussion focuses on calculating the new angular speed and energy lost to friction when four children sit on a spinning merry-go-round. The initial angular speed is 0.40 rev/s, and after the children sit down, the new angular speed is found to be 0.17 rev/s. The total mass changes from 17.86 kg to 117.86 kg, leading to a calculated energy loss of 260 joules. The initial confusion stemmed from a misunderstanding of the merry-go-round's dimensions, specifically the diameter versus radius. The calculations were ultimately corrected, confirming the energy loss due to friction.
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Homework Statement



A 2.8-m-diameter merry-go-round with rotational inertia 140kg⋅m2 is spinning freely at 0.40rev/s . Four 25-kg children sit suddenly on the edge of the merry-go-round.

a) Find the new angular speed.

b) Determine the total energy lost to friction between the children and the merry-go-round.

The Attempt at a Solution



a) 0.17rev (verified)

b) The old mass is 17.85714286kg, old angular speed is 2.513274123 ms-1
The new mass is 117.85714286kg, new angular speed is 1.066237507ms-1

To find the change in energy:

0.5(117.85714286kg)(1.066237507ms-1)2 - 0.5(17.85714286kg)(2.513274123 ms-1)2

The answer is 260j but I'm not getting it.
 
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Managed to solve it. I made a slip. It was 2.8m diameter instead of 2.8meter radius.:devil:
 
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