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

In summary, a 2.8-meter diameter merry-go-round with a rotational inertia of 140kg⋅m2 is spinning freely at 0.40 revolutions per second. When four 25-kg children suddenly sit on the edge, the new angular speed is 0.17 rev, and the total energy lost to friction between the children and the merry-go-round is 260 joules.
  • #1
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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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  • #2
Managed to solve it. I made a slip. It was 2.8m diameter instead of 2.8meter radius.:devil:
 

1. What is rotational inertia?

Rotational inertia is the resistance of an object to changes in its rotational motion. It is determined by the mass and distribution of the object's mass around its axis of rotation.

2. How does rotational inertia affect energy loss due to friction?

As the rotational inertia of an object increases, the amount of energy lost to friction also increases. This is because a higher rotational inertia means there is more mass distributed around the axis of rotation, resulting in more frictional forces acting on the object.

3. What factors contribute to changes in rotational inertia?

The main factors that contribute to changes in rotational inertia are the mass and distribution of the object's mass. Other factors such as the shape and size of the object can also play a role.

4. How does friction affect the amount of energy lost due to changes in rotational inertia?

Friction causes a loss of energy in any type of motion, including rotational motion. The amount of energy lost due to changes in rotational inertia is directly related to the amount of friction acting on the object.

5. Can the amount of energy lost due to changes in rotational inertia be reduced?

Yes, there are ways to reduce the amount of energy lost due to changes in rotational inertia, such as using lubricants or reducing the friction between surfaces. Additionally, reducing the mass and distribution of mass in an object can also help decrease the amount of energy lost.

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