To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × 10⁷ J of energy.Suppose we tried to store this much energy in a spinning,solid,uniform,cylindrical flywheel.A large flywheel cannot be spun too fast or it will fracture.If we used a flywheel of diameter 1.2 m and mass 400 kg,what angular speed would be required to store 3.2 × 10⁷ J? A)1800 rad/s B)3600 rad/s C)940 rad/s D)530 rad/s E)5500 rad/s

Question

Quizplus · Accepted Answer

The moment of inertia of a cylindrical flywheel is given by:
I = (1/2)mr^2
where m is the mass and r is the radius of the flywheel.

Using the given values, we get:
I = (1/2)(400 kg)(0.6 m)^2 = 144 kg m^2

The angular speed required to store 3.2 × 10^17 J of energy is given by:
K = (1/2)Iω^2
where K is the kinetic energy stored and ω is the angular speed.

Setting K equal to 3.2 × 10^17 J and solving for ω, we get:
ω = √(2K/I) = √[(2)(3.2 × 10^17 J)/(144 kg m^2)] = 940 rad/s

Therefore, the best choice is C, 940 rad/s.

To Drive a Typical Car at 40 Mph on a Level