Calculate the power needed to spin a flywheel?

Question

Can you check my work please? 

The energy E needed to spin up a flywheel from rest is E = 0.5 I ω ^2
where I is the moment of inertia and ω is the new speed. (in radians/sec)

Lets look at spinning up a lathe chuck to 400 rpm. 

400 rpm = 400 * 2 * pi / 60 = 42 radians per second.

I = 0.5 m r^2. so a 10kg chuck of 0.2m dia has I = 0.5 *10 *0.1^2 = 0.05

E = 0.5 * 0.05 * 42^2 = 44.1 Joules. To get this up to speed in 10 seconds uses 44.1/10 = 4.41 Watts.

I cant believe a 5W motor would be able to do this.  Is my woking right?

Dean · Accepted Answer

Your maths checks out, but : energy change / time = average power

Try this for instantaneous power required  :
(constant acceleration is assumed)

First find the rotational acceleration rate from ( 42.0 - 0 ) / 10 =  4.2 rad / sec /sec

The torque required to accelerate the 10 kg chuck at this rate
 = mass moment of inertia *  rotational acceleration rate 
 = 0.05 * 4.2 = 0.21 Newton - meters

instantaneous power consumption =  torque * max rotation rate = 0.21 * 42 = 8.82 Watts

Thats all i have 
Hope it helps

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Calculate the power needed to spin a flywheel?

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