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
short answer ;
angular velocity is same for each point of the ball.
linear/tangential velocity is directly propotional to distance from center.
Long Answer;
All the points of a rotating ball cover equal angle in ,say, one second. If a point at center covers an angle of 90 degrees, a point on outside must also cover the same angle! (as its a rigid body). But, here’s the fun part, the part on the outer side has to cover more distance “naturally” then the one on inside in same time. So the velocity of outside point must be higher so they can cover equal angles.
And as, equal angular displacment is covered, we can say angular speed is same.
source; im a high school student
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