How Can I Calculate Flywheel Spin-Up Time for Various Mass and Shape Options?

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TheSilverhead
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Hello! I've got a problem that I haven't the faintest clue how to go about. I have a flywheel, spinning on a motor's shaft. I want to be able to calculate the time it will take the flywheel to spin up to the motor's max RPM, based off of the variables:
Motor's RPM
Motor's Toque
Flywheel's mass
Flywheel's shape (Solid disk, disk with outer ring, etc.)
Flywheel's diameter.

I have a fixed motor, with enough amperage that it will always be able to draw as much as it needs (from stall.) I'm varying the flywheel's mass and shape to find a good balance of low spin-up time to high stored energy. The flywheels are used to propel items, if it matters.

Thanks!
 
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For an idealized electric motor, peak torque occurs at zero rpm and the torque decreases linearly to zero as rpm increases linearly to max rpm. I'm wondering if in this idealized case, the time to reach max rpm will be infinite (I didn't do the math). The time to reach some rpm close to max rpm will be finite.
 
Why are you concerned with the flywheel?
You say that your aim is to propel items, sort of a mass driver idea I guess.
The main benefit of the flywheel is to moderate the RPM swing when the ejected mass separates from the launcher. But there is no real advantage to having lots of stored energy in the flywheel otherwise.
Of course you can add some contraption to help transfer the flywheel energy to the 'flight item', but that is a very different discussion.
 
Not sure if this will help, but take a look if you don't mind:

Angular acceleration = torque / Angular inertia (also known as Moment of inertia)

here is something that will help you out on calculating the angular inertia of your disk: http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html

Ask for more if you want, angular motion has sort of become my expertise after spending most of my time on this forum for it.