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

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To find the equivalent point mass for a rotating disk, one must consider the radius of gyration, which accounts for the distribution of mass around the axis. The radius of gyration is less than the disk's radius, as not all mass is located at the outer edge. This radius is crucial for calculating angular acceleration and other rotational dynamics. The concept emphasizes that while the mass cannot be simplified to a single point without affecting stability, it can be modeled as a ring with the same mass and an appropriate radius of gyration. Understanding this relationship is essential for accurate rotational motion calculations.
mather
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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
 
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hello mather! :smile:
mather said:
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 :redface:), 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" :wink:
 
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