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Calculate the power needed to spin a flywheel?
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?
Thanks for the prompt response Dean!
I still find it hard to believe a rotating lathe chuck stores only 44 watt seconds of energy!
2 Answers
- DeanLv 68 years agoFavorite 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
