OT/chinton ...[He starts standing up,then as he spins, he squats down.What happens?He spins faster.Is the earth squatting down?]
As a child I used to wonder how this could be. It appeared to be nothing short of amazing. In fact it is nothing short of straight forward physics.
The skater changes their moment of inertia, by varying body position/shape. If they start spinning slow with legs and arms outspread, their rotational inertia is much greater than when they pull their arms and legs in close to their body. Inertia is related to mass and distance squared from the center axis of that point mass. Once they start spinning and quit adding energy, the difference in rotational speed is related linearly to the change in inertia, which can change a lot due to the mass and distance squared relationship. This is exclusive the losses due to air and blade friction, which over a short time period are minimal.
So actually they spin fastest when they stand like a pencil and suck their arms and legs as close as possible to a center axis position. A skinny skater can really get going. They come to a quick stop by extending arms and legs, and applying blade friction. The squatting doesn't really have much to do with it, other than how it facilitates the position of the arms and legs and their distance from the center axis of rotation. As I recall they usually go into a spin at the end of 'run', in a semi-crouch position. This gives them energy in so to speak, at an initial spin speed with a high value of rotational inertia. They then suck all their limbs in and stand like a pencil, greatly reducing rotational inertia and increasing spin speed. About the time they get dizzy (I suspect) they extend limbs again in a pattern (reduces spin speed) and sort of bow, dig blades in and stop. Conservation of mass must be maintained (unless they spin really really fast).
If the rotational speed of the earth were to change, it would probably be due changes in mass and mass distribution, about the center axis. If the earth squatted, or if the distance between the geographical poles decreased, the spin speed would slow, barring some additional energy input. As I recall the earth is actually shaped a little like a pear.
Remember the old tether ball on the pole, and how fast it would wind up toward the end, when the rope got short? Same principal.
Just thought I'd help. |
