# Homework Help: Rotational Kinetic Energy -> Lightning Speed Running?

1. Sep 27, 2007

### eraemia

1. The problem statement, all variables and given/known data

Suppose a solid cylindrical flywheel has a mass of 200 kg and a radius of 0.8 m and rotates at a rate of 15,000 revolutions per minute. If you were able to convert all of its rotational kinetic energy into making you run, how fast would you be going? (Assume your mass is about 65 kg).

2. Relevant equations

Moment of inertia of solid cylinder:
I = (1/2)MR^2

Rotational kinetic energy of a rotating object:
Krot = (1/2)Iw^2

Kinetic energy:
K = (1/2)mv^2

3. The attempt at a solution

M = 200 kg is mass of solid cylindrical flywheel
m = 65 kg is my mass
R = 0.8m
w = 15000 rev/min = 250 rev/s = 500*pi*rad/s

Find moment of inertia of solid cylindrical flywheel:
I = (1/2)MR^2
I = (1/2)(200 kg)(0.8)^2
I = 64 kg*m

Find rotational kinetic energy of solid cylindrical flywheel:
Krot = (1/2)Iw^2
Krot = 7.9 * 10^7 J

If Krot = K, then solve for v:
Krot = K = 7.9 * 10^7 J
K = (1/2)mv^2
v = sqrroot[ (2K) / m]
v = sqrroot[ (2*7.9*10^7 J) / 65 kg ]
v = 1559 = 1600 m/s

Can I set Krot = K like that? Is my approach to this problem correct? Thanks a lot for the help!
EDIT: The velocity figure looks weird...Nobody can run that fast... Where did I make a mistake?

Last edited: Sep 27, 2007
2. Sep 27, 2007

### eraemia

Or do I find v with v = rw? (but that wouldn't relate to energy? I'm terribly confused)

3. Sep 27, 2007

### mgb_phys

That is the correct way to do it ( haven't checked arithmateic)
Nobody can run that fast, but they also can't carry a 200kg flywheel running spinning at 250Hz! Large flywheels store a lot of energy - and can dump it very quickly.

4. Sep 27, 2007