Find the Diameter of an Iron Disk for Kinetic Energy Storage of 14.6

[chrismcr]

Diameter of disk?

Question: Consider a flywheel made of iron, with a density of 7800 , in the shape of a uniform disk with a thickness of 12.4 . What would the diameter of such a disk need to be if it is to store an amount of kinetic energy of 14.6 when spinning at an angular velocity of 91.0 about an axis perpendicular to the disk at its center?

I know that I=.5mr^2 for the disk, I just don't know how to apply that towards getting a solution for work?

I have pondered this question for some time now, and I know I am just missing one piece, i just don't know what it is. Any help would be greatly appreciated. Thanks

 

[OlderDan]

Surely you were not given a problem with all those quantities stated with no units. State the units that go with those numbers. What is the energy of a rotating rigid object?

 

[chrismcr]

im sorry..here are the units.
7800kg/m^3
14.6MJ
12.4cm
91RPM

The energy of a rotating object would have to be..
=.5mv^2+.5Iw^2

 

[OlderDan]

im sorry..here are the units.
7800kg/m^3
14.6MJ
12.4cm
91RPM

The energy of a rotating object would have to be..
=.5mv^2+.5Iw^2

For a flywheel, only the rotational energy is of interest. The first term is for translational motion of the CM of the disk, and either there is no such motion or you don't care about it because it is not part of the "stored energy". You know how to find the I of the disk and you can convert the RPM to ω. You can write the mass of the disk in terms of its density and volume, and you can write the volume in terms of the thickness and radius of the disk Put all that into the energy equation with the energy given and solve for R, then find the diameter.