# How many accelerations from a speed of zero to 12 m/s could the car make before the flywheel's energy was dissipated?

The U.S. Department of Energy had plans for a 1500-kg automobile to be powered completely by the rotational kinetic energy of a flywheel. The 300-kg flywheel (included in the 1500-kg mass of the automobile) has a 6.0-kg⋅m2 rotational inertia and can turn at a maximum rotational speed of 3600 rad/s.

I found the maximum rotational kinetic energy which is:

3.9x10^7 J

I'm just unsure how to approach the question asked above.

### 3 Answers

- NCSLv 72 years agoFavorite Answer
The KE acquired by the car at 12 m/s is

KE = ½ * 1500kg * (12m/s)² = 1.08e5 J

So, how many times does this value go into 3.9e7 J?

Hope this helps!

- oubaasLv 72 years ago
Stored energy in the flywheel Ekf :

Ekf = J/2*ω^2 = 6/2*3.6^2*10^6 = 3.8880*10^7 joule

stored energy in the car each acceleration Ekc :

Ekc = m/2*V^2 = 0.75*10^3*1.2^2*10^2 = 1.080*10^5

n = Ekf/Ekc = 360.0 times