Power and torque what did i do wrong?

[ahello888a]

power and torque what did i do wrong?

Homework Statement

A rotating uniform cylindrical platform of mass 230 kg and radius 5.6 m slows down from 3.8 rev/s to rest in 16 s when the driving motor is disconnected. Estimate the power output of the motor (\rm hp) required to maintain a steady speed of 3.8 rev/s

Homework Equations

Wfriction=change in KE = -.5*I*w^2
power=work/time

The Attempt at a Solution

So I was was able to get the amount of work that the friction force does and it was -.5 (.5 * MR^2)w^2 = 45053.39J and that work done by friction is the same amount of work needed for the motor to output. So the power of the motor needed is 45053.39/16s = 2690.8Watts and to convert that to HP I just divide by 746W and got 3.6HP. is that right?

 

[mukundpa]

I fear the calculation for energy is not correct, Please recalculate. (Don't forget to convert rev/s into radians/s)

 

[ahello888a]

is it 86.12HP? I guess I did forget to do that conversion, but is the method correct?

 

[alphysicist]

HI ahello888a,

Homework Statement

A rotating uniform cylindrical platform of mass 230 kg and radius 5.6 m slows down from 3.8 rev/s to rest in 16 s when the driving motor is disconnected. Estimate the power output of the motor (\rm hp) required to maintain a steady speed of 3.8 rev/s

Homework Equations

Wfriction=change in KE = -.5*I*w^2
power=work/time

The Attempt at a Solution

So I was was able to get the amount of work that the friction force does and it was -.5 (.5 * MR^2)w^2 = 45053.39J and that work done by friction is the same amount of work needed for the motor to output. So the power of the motor needed is 45053.39/16s = 2690.8Watts and to convert that to HP I just divide by 746W and got 3.6HP. is that right?

I don't believe this is the correct approach. This power that you are finding here is the average power from the frictional torque during the entire slowing down process. But while the speed is decreasing, the power from friction is also decreasing.


So here you need the power at the beginning of the slowing down process. What is the formula for the instantaneous power (for the rotational case)?