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 a fantastic question because all speed is relative. It depends on where you are measuring from.
Correct. That is why in physics rotation is measured in both radians/sec and actual velocity at a point.
I consider this like a merry-go-round or a rotating circle. A point on the edge has a longer distance to travel to return to that same place than nearer the centre. The absolute centre on its axis does not have to travel anywhere. A rolling wheel travels further in one revolution the larger its circumference becomes.
A sphere is a 3D shape defined by a single distance from a point but still rotates around the same 1D axis with the same rules. A slice made through that sphere would produce a 2D circular intersection with the same properties as that circle from big, through smaller to a point at the poles where the axis intersects.
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
nobody has mentioned the coriolis effect, what you say regarding the speed in Ecuador is correct and generates a very interesting effect called the coriolis effect in general terms due to the difference in speeds in the different latitudes, look it up it is very interesting
Yes. Every point in a ball’s surface (except for poles) goes around the axis making a circular orbit. The diameter of this circle is smaller closer to the axis and bigger further. Every point moves around with the same speed but the ones further has a longer route to do in the same time amount thus has to move faster than the closer ones.
points closer to the axis of rotation move slower for the same angular speed, points on the axis are immobile.
linear speed = angular speed * distance from the axis.
[removed]
If you are talking about linear velocity (m/s), yes the outer the edge, the faster. But if you are talking about angular velocity (change in angle over time. Measured in rad/s), then they are all the same.
take the sphere. then imagine an axis, like a cilinder rod, passing through the middle of the sphere. the farther you are from that axis, horizontally, the faster you will go, because you’ll need to cover the same angle at the same time, but in a greater perimeter (distance). the closer you are to that axis, the slower you move, because the perimeter is smaller. all parts of the sphere rotate at the same time, but specific points in the circle will be faster or slower depending on how far away from the central axis they are.
Latest Answers