How Can We Calculate the Radius of Gyration for a Rotating Disk?

[mather]

hello

imagine a disk rotating by an axis that passes through the center of the disk

how can we find the analogue of a mass rotating by an axis?

I mean, how can we lump the whole mass of the wheel to a point?

how much will be the distance of this point from the axis?

for example to rotate a disk with radius 10 and mass 100 you need the same force as to rotate a point of mass 100 and rotation radius = ??

I suppose the radius will be some less than 10 (since not all parts of the disk are at this radius), but how much exactly?

thanks

PS: we need to do this in order to calculate other things, eg angular acceleration, etc

 

[tiny-tim]

hello mather!

imagine a disk rotating by an axis that passes through the center of the disk
… how can we lump the whole mass of the wheel to a point?

how much will be the distance of this point from the axis?

We can't lump it to a point (because it needs to have the same centre of mass as the disc, otherwise it will wobble ), but we can lump it to a ring, with the same mass as the disc, and whose radius is the radius of gyration …

see http://en.wikipedia.org/wiki/Radius_of_gyration"