I`m making a flywheel and with the math

[CWatters]

Had a quick look and the sums seem ok.

If the output torque is 3.68 N.m then I think the required input torque is going to be four times that or about 10 N.m

If the input is 20rpm (= 0.7∏ rads/s) then I make the power required about

P = 0.7∏ * 10 = 22W

but just for the 0.25 seconds it takes to spin up.

Perhaps best design it assuming the current to your motor might spike to say 100W briefly to give plenty of margin?

 

[wheelslave1]

Why is there such a big difference between linear acceleration and circular acceleration?

So...the answer is 7.4ft-lbs of torque on the 6in main cog. Also need to order a motor that can spike 100W.

 

[jbriggs444]

Why is there such a big difference between linear acceleration and circular acceleration?

There's not much difference. It's just a matter of leverage.

If you keep a wheel the same size and push farther out toward the rim, you get more leverage on the wheel.

If you make the wheel bigger and keep pushing at the same point, the wheel gets more leverage on you.

 

[mfb]

Ok, I think I get the idea now.

And it leads to an interesting theorem: No gear can have a perfect axial symmetry.Consider the following setup: Three wheels on top of each other, with the same axis, but not locked in their rotation. Assume that there is no loss when they spin. The middle wheel B can be moved vertically to slide on either the lower (A) or the upper (C) wheel. Build some gear to force a 4:1-ratio of the angular velocity of the wheels C and A.

Let the middle wheel B slide on the lower wheel A, accelerate them until they rotate with 20 rpm - the top wheel C will rotate with 80 rpm now. Now lift B until it slides on C: B will accelerate, A and C will slow down. Friction leads to some heat. As soon as the system is in equilibrium, lower the (fast-rotating) B until it slides on A: B will slow down, A and C will accelerate. Friction leads to some heat, so the total energy is lower than before. But at the same time, the setup is identical to the initial conditions - A and B move with the same angular velocity and C with 4 times that value. It is isolated from the environment, so momentum conservation gives 20 rpm for A and B and 80 rpm for C.
What is wrong?

Spoiler

I did not account for the gear. It has to have some external anchor which is not on the same axis, and can exchange angular momentum with the environment.

 

[CWatters]

Why is there such a big difference between linear acceleration and circular acceleration?

There is no difference really. If you drop a steel ball onto a thick steel plate the g forces can be very very high.

Consider designing your mechanisim to prevent the "white rod" stopping rapidly. Perhaps using a soft rubber bump stop. The longer the stopping distance (or time) the lower the torque.