eli5 Does every part of a ball spin at the same speed?

Question

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

Answer 1

Rate = distance/time. (Think miles or km per hour, right? Written km/h.)

If you look at a solid disk and spin it one revolution, a point very near the center is going to travel in a much smaller circle than a point on the outer edge.

If you take both those circles and break them and flatten them out I to straight lines you can measure the linear distance traveled. Both did one revolution, which means they moved for the same amount of time. in the same amount of time.

So if the time is the same, and the distances are different, than the speeds have to be different, right?

In mathematical terms, looking at the S = D/t formula the speed is directly proportional to the distance, and inversely proportional to the time. So if the distance goes up then the speed goes up. If the distance remains the same but the time goes down, then the speed goes up.

To think about that intuitively,if you walk a mile in one hour, you went 1 mph. If you walk twice as far in the same hour, you went 2 mph. Conversely, if you walked a mile in just half an hour, then you must have been walking at a rate of 2 mph. Because if you kept walkingat the same rate for a full hour you would have gone two miles, right?

So, yeah, when you’re closer to the axis of rotation of a solid body your linear speed is slower than if you’re further out because you are traveling less linear distance.

Which is why when you start spinning things you need different terms for rates and you can talk about number of revolutions over time, or rotational speed, or radial speed, etc.