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
This is one of those cases where a complete answer is about as easy as the ELI5. More of an ELI15, but I’m sure you’ll follow:
A ball spinning on its axis has what’s called Angular Velocity. We call the Angular Velocity w.
The ball spins about an axis. For any point on (or in) the ball distance d (measured perpendicular from the axis), the speed of that point is simply
2 * pi * w * d
So if you have a 2″ ball (1″ radius), spinning at 100 rpm, a point on the “equator” of the ball will be moving at
2 * 3.14 * 100 rpm * 1 in = 628 in/minute
A point near the top of the axis, 1/8″ from the axis will be spinning
2 * 3.14 * 100 rpm * 1/8″ = 78.5 in/minute
It’s that easy.
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