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.
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take a look at a bike tire or any other wheel. mark a point on it close to the axle and another point on the tire. spin the tire. you will see that both points cross their original positions at the same time. now consider the circumference of the circle made by the point close to the axle. it is much less distance than the circle made by the point on the tire. therefore, the further the point is from the axis, the farther it has to travel for one full spin. if it does that in the same amount of time, it must be traveling faster.
It spins at the same rotational speed throughout, but the tangential (or linear) speed changes depending on where you are looking at the ball.
Let’s say you’re on the Earth. The entire Earth rotates 360°/day, that’s 15°/hour or π/12 radians per hour. It doesn’t matter where you are on Earth for this.
If you’re 1m from the north pole, you will travel in a circle of circumference 2π m (6.28m) over the course of a day. That’s π/12 m/hr (.26m/hr or .00026 kph)
If you’re at the equator, you are 6.378×10^6 m from the axis of rotation, so over the course of a day, you travel in a circle of circumference of about 40,000 km. That’s a speed of 1670 kph.
Radially (d in radians), yes. The earth rotates at π/12 Radian/h anywhere along any axis.
Linearly (d in meters), no. Any point on earth rotates at r*π/12 km/h where r is the straight-line distance from said point to the North/South Pole Axis.
… Except anywhere along the North/South Pole Axis itself. Those do not move through space at all, so their speed is 0 radian/h (and 0 km/h because r=0).
… If you don’t take into account the fact that the Earth is orbiting the sun, and the sun is orbiting Sagitarius A*, and the universe is expanding, of course.
Your understanding is correct. There are rings on the surface of the circle where the radius from the axis of rotation is equal all the away around, but as you change the distance from the axis of rotation, the speed changes equivalently. This is why on earth the poles barely move and the equator is always rotating. They spin at the same rate, but the speed they move is different.
Angular velocity = Angular rotation x distance from axis of rotation
That is why radians where invented and when you get into complex math to do with spheres it all becomes radians. Radians are a conveniwnt way tp measure rotation around a circle, and makes the math easier.
That would depend on what you mean by “speed”. “Speed” usually refers to how far something travels in a given time, but it can also refer to how much it rotates in a given time (angular speed).
Every part of the ball has the same *angular speed*. It’ll take the same amount of time to complete one revolution. Not every part will travel the same distance in the same amount of time.
On Earth, this means that a day is the same length of time no matter where you are. Whether you’re in the arctic, the tropics, on top of a mountain, or deep below ground, a day is the same amount of time. However, the distance you travel over a given time period will depend on where you are. You’re fastest at the equator, you’re stationary at the poles. You’re fastest on a high mountain, you’re stationary at Earth’s core. If you’re on the rotational axis, you’re stationary, and you’ll move faster the farther you are away from it.
Relevant explanation regarding car wheels from [Neil Degrasse Tyson](https://youtube.com/shorts/LrORYLjVaTU?feature=share)
Yes and no.
**The Yes:** Every atom of the ball is spinning at the same **rotational speed**.
**The No:** The atoms further from the center are moving faster than the ones closer – they **cover more distance in the same unit time**. The atom exactly at the center of the spin is not moving in space at all ( only around its own axis ).
So, depending on what speed you are measuring the answer is yes or it is no.
Yes. Imagine you spin a chain around above your head. When it makes one full spin, every link has only gone around once. Links by the hand have traveled less distance than those at the end. So those at the end must have been moving faster to cover more distance in the same time frame.
Yep.
I’m not a physisist or anything, but in my head I’m almost certain that they do, imagine you put a dot on the equator of the ball and a dot directly above it near one of the balls poles, and you spin it.
If different parts of the ball spun at different speeds, both dots would eventually become misaligned, but obviously they don’t. Both dots stay in the exact same position relative to each other during the entire spin.
This is why most rocket launches are near the equator, and launch in the same direction. We get a big speed bump from equitorial launch speeds.
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