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

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SUMMARY

The discussion focuses on calculating the energy lost to friction when children sit on a spinning merry-go-round. The initial parameters include a 2.8-meter diameter merry-go-round with a rotational inertia of 140 kg⋅m² and an initial angular speed of 0.40 rev/s. After four 25-kg children sit on the edge, the new angular speed is calculated to be 0.17 rev/s. The total energy lost to friction is determined to be 260 joules, correcting an earlier miscalculation related to the diameter versus radius of the merry-go-round.

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  • Understanding of rotational inertia and angular momentum
  • Familiarity with energy conservation principles
  • Basic knowledge of rotational kinematics
  • Ability to perform calculations involving joules and revolutions per second
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  • Learn about energy transformations in rotational systems
  • Explore the effects of friction on rotating bodies
  • Investigate the relationship between mass distribution and rotational speed
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Physics students, mechanical engineers, and anyone interested in the dynamics of rotating systems and 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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