How Fast Must a Flywheel Rotate to Store 1.4 x 10^9 J?

[mikefitz]

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk and its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 387-mile trip in a typical midsize car produces about 1.4 x10^9 J of energy. How fast would a 16-kg flywheel with a radius of 0.22 m have to rotate in order to store this much energy? Give your answer in rev/min.

I know the kinetic energy of a flywheel is: http://content.answers.com/main/content/wp/en/math/1/4/8/148da762c81d0061d84cb36a21fb1e4e.png but how do I use that information to calculate how fast the flywheel needs to rotate? Thanks

 

[OlderDan]

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk and its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 387-mile trip in a typical midsize car produces about 1.4 x10^9 J of energy. How fast would a 16-kg flywheel with a radius of 0.22 m have to rotate in order to store this much energy? Give your answer in rev/min.

I know the kinetic energy of a flywheel is: http://content.answers.com/main/content/wp/en/math/1/4/8/148da762c81d0061d84cb36a21fb1e4e.png but how do I use that information to calculate how fast the flywheel needs to rotate? Thanks

What is the definition of ω?

 

[FredGarvin]

Rearrange your equation to solve for omega. Do you know what each variable in that equation represents?

 

[mikefitz]

E=1.4*10^9 J
m=16kg
r=.22m

I=.5*16kg*.22^2 = .3872

1.4*10^9=.5*.3872*w^2

w=85037.67 rev/min?

 

[OlderDan]

E=1.4*10^9 J
m=16kg
r=.22m

I=.5*16kg*.22^2 = .3872

1.4*10^9=.5*.3872*w^2

w=85037.67 rev/min?

ω is in radians/second. If you had included the units in your calculation, you would have found the answer to have units of 1/s. The radians are a dimensionless quantity we add to the result because we know they were used in deriving the kinematic equations or rotation. You need to convert radians per second to revolutions per minute.