Conservation of Energy with Rotation Video Lessons

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Problem: Use conservation of energy to determine the angular speed of the spool shown in Figure P8.52 after the 3.00-kg bucket has fallen 4.00 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds.

FREE Expert Solution

In this problem, we have gravitational potential energy, linear kinetic energy, and rotational kinetic energy. 

Using conservation of energy:

K0+U0+Wnc=Kf+Uf, where Wnc is the work done by non-conservative forces such as friction.

Linear kinetic energy:

K=12mv2

Rotational kinetic energy:

K=12Iω2

Gravitational potential energy:

U=mgh

Moment of inertia of the spool:

I=12MR2

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Problem Details

Use conservation of energy to determine the angular speed of the spool shown in Figure P8.52 after the 3.00-kg bucket has fallen 4.00 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds.

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