I was holding a rubber band ball in my hand earlier and tossing it up in the air at about eye level. I noticed that I could see the shape of individual rubber bands on the axis of rotation on the outside of the ball but the edges of the ball were blurry. This got me thinking.. is a ball spinning slower near the axis than it is at the outer edge? Is the earth spinning faster at the equator than it is at the poles? If speed is d/t then the math makes sense to a layman like me that the ball would be rotating slower at the center and faster on the edges. Please help.
edit: holy shit. balls are fascinating.
In: 439
Let’s ignore real physics and assume you have a perfectly rigid ball spinning in space, because it’s easier to answer your underlying question that way.
In that case, no part of the ball is spinning faster in an angular sense; that is, every part of the ball is moving the same angle of rotation in the same amount of time (with the exception of the line through the ball which defines the axis of symmetry, which isn’t moving).
However, different parts of the ball are definitely spinning at different speeds in the sense of distance traveled. If you look at the outside of the ball, it has to cover a distance of 2 pi R for every time the ball rotates, where R is the outer radius. But if you look at a piece that’s closer to the axis of rotation of the ball, it needs to travel less distance. And if you look at the point at the top and bottom of the spinning ball, it’s not moving at all. And yes, this happens on Earth. The apparent force of gravity is slightly larger at the North Pole and the South Pole than it is at the equator. Some of this is because the Earth itself bulges around the equator. Some of it is because, the further you are away from the axis of rotation, the more force of gravity has to go towards keeping you on the surface of the Earth rather than pulling you into the Earths surface.
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