# What is the Angular Speed of the Spool After the Bucket Falls?

• Touchme
In summary, using conservation of energy, the angular speed of the spool can be determined after the 3.00 kg bucket has fallen 4.65 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds. By considering the initial and final energies, the final angular speed can be solved for using the equation (KEr + KEt + mgh)i = (KEr + KEt + mgh)f. After correcting a mistake in the mass used for the kinetic energies, the final angular speed is found to be 14.06 rad/s.
Touchme
Use conservation of energy to determine the angular speed of the spool shown in Figure P8.36 after the 3.00 kg bucket has fallen 4.65 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds.

I used conservation of energy.
(KEr + KEt + mgh)i = (KEr + KEt + mgh)f
0 + 0 + (3 x 9.8 x 4.65) = [.5(.5Mr^2)w^2] + .5(Mv^2) + 0
136.71 = (.25Mr^2)w^2 + .5Mv^2
136.71 = (.25 x 5 x v^2) + (.5 x 5 x v^2)
v = 7.39
w = 12.324

The ans is not correct, what am i doing wrong?

Thank you for lookin but I manage to see my mistake. I used the wrong mass for the KEt

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and KEr. The mass for the KEt and KEr should be the mass of the bucket only not the spool and the bucket. 0 + 0 + (3 x 9.8 x 4.65) = [.5(.5Mb^2)w^2] + .5(Mbv^2) + 0136.71 = (.25Mb^2)w^2 + .5Mbv^2136.71 = (.25 x 3 x v^2) + (.5 x 3 x v^2)v = 6.753w = 14.06

term. It should have been the mass of the bucket (3 kg) rather than the total mass (5 kg). The correct calculation would be:

(KEr + KEt + mgh)i = (KEr + KEt + mgh)f
0 + 0 + (3 x 9.8 x 4.65) = [.5(.5Mr^2)w^2] + .5(Mv^2) + 0
136.71 = (.25Mr^2)w^2 + .5(3v^2) + 0
136.71 = (.25 x 5 x v^2) + 1.5v^2
v = 7.39 m/s

This is the correct answer for the angular speed of the spool after the bucket falls. It is important to carefully consider all the terms and their corresponding masses when applying conservation of energy equations.

## 1. What is rotational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation around an axis. It is dependent on the object's moment of inertia and angular velocity.

## 2. How is rotational kinetic energy calculated?

The equation for calculating rotational kinetic energy is E = 1/2 * I * ω^2, where E is the energy, I is the moment of inertia, and ω is the angular velocity.

## 3. What factors affect rotational kinetic energy?

The main factors that affect rotational kinetic energy are the object's moment of inertia and angular velocity. Other factors include the mass distribution of the object and any external forces acting on it.

## 4. What is the difference between rotational and translational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation, while translational kinetic energy is the energy an object possesses due to its linear motion. They are both forms of kinetic energy, but they are calculated and measured differently.

## 5. How is rotational kinetic energy related to work and power?

Work is the transfer of energy, and power is the rate at which work is done. Rotational kinetic energy can be related to work and power in the context of rotational motion by considering the work done by a torque on an object and the power required to maintain a constant angular velocity.

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