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Comment by sandworm101 | Hacker News Reader

What is amazing is the rotational speeds involved. Say the flywheel weighed as much as a tesla. Think of the energy. Say you want to store enough energy so that a tesla can accelerate itself from zero to 100mph ten times. That amount of energy in a flywheel weighing the same as the tesla would mean the flywheel spinning at +/- 1000mph. Either this flywheel weighs hundreds of tons, or it is spinning at supersonic speeds. Either way, you better have some good bearings.

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The magical word here is „angular momentum“. The energy that a chunk of mass can store in a flywheel is squared with the distance of that mass to the center of its rotation axis. If you distribute the Tesla sized mass around the edges of a 4m sized Flywheel now (spare a few % for the wheel and structural support), it can store quite a few dozen times the energy of the same sized Tesla going the same speed.

I'm pretty sure it doesn't matter whether the eneergy is stored in rotating body, or one moving in a straight line. Kinetic energy of rotation is 0.5 * I * w^2, or for that extreme case of "concrete ring" - 0.5 * m * r^2 * w^2, which is exactly equal to 0.5 * m * v^2, or kinetic energy as calculated for body moving in straight line.

Are you sure that you aren't confusing force with energy? Angular or not, it's just accelerated mass.

So let's do a little high school "perfectly spherical cow of uniform density" physics here.

Imagine we take that 1 Tesla mass and turn it into a infinitely thin ring of infinite density material. Now we can calculate how fast it's need to be spinning to get all that mass doing "1000mph".

Lets make our infinitely dense 1 Tesla mass into an infinitely thin ring 1m in radius. Each point on that ring moves around it (2pir) circumference every revolution so ~6.3m per revolution. 1000mph =~ 440m/s SO we only need to spin this flywheel ay ~70 revolutions per second, just over 4000RPM.

4000RPM doesn't seem unreasonable...

(Note:I don't think your 1000mph stacks up though. The kinetic energy of a moving mass is 1/2mv^2. So the speed of a 1 Tesla mass object which has 10 times the energy of a 1 Tesla object doing 100mph is only sqrt(10)*100 closer to 320mph than 1000. My high school physics flywheel might only need to spin at 1500RPM...)

Modern flywheels spin extremely fast in a vacuum, so supersonic is moot.

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