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An apple rolling

  1. Nov 9, 2012 #1
    I was walking down the street kicking and apple (why? I don't know) and I noticed that an apple, after a couple of bounces, always rolls on its side. It doesn't roll over it's stem continuosly. I was wondering why?
  2. jcsd
  3. Nov 9, 2012 #2

    Simon Bridge

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    Because of it's shape.

    Simpler case: watch a football (the oval kind) roll - try making it roll end-over-end.
    One way is unstable - small changes in the situation will knock it off that line.
  4. Nov 10, 2012 #3
    Well, yes, the shape... but you have to say more than that. In fact, more than I will say because I know little.

    The typical apple has its largest radius around its "equator" if you call the stem end the North pole.
    When you kick it, its movement across the ground produces friction, which puts the apple in a spin...
    For an object that is close to round and uniformly dense, any random initial spin orientation that does not position the additional mass of excess radius deviations furthest from the axis of rotation will be subject to torques that act to do so... There is a Coriolis effect when the excess mass of the larger radial distance locations are not aligned to the rolling ground contact line around the apple.

    In the apple, the "equatorial" line described above comprises those locations furthest from the center and their addition mass and longer lever arm will torque the axis of rotation until the axis of rotation is through the stem and its opposing counterpart - whatever that little belly button thing is called opposite the stem.

    So basically, the apple spin axis is stable when the most mass is furthest from the axis of rotation... that "most furthest mass" is "equatorial" but it can't redistribute so the Coriolis torques shift the axis to be "polar" through the stem.
    Because the apple is rolling, the friction and the longer lever arms of the excess radial deviations are additionally acting to torque the axis of rotation... perhaps a little chaotically until stable reorientation is complete?

    Now, the radial deviations are really about mass distribution from the center of mass, and density if that varies. In the apple, the density is close to uniform, but in the football there are two differences.
    1] The density is not uniform, it is a skin holding air. The football has multiple stable spin axes because of physical symmetries and a more complex mass distribution because of its shape and because it is hollow.
    2] It includes the behavior that one of its preferred orientations of spin axis is through the long axis which does NOT place the longest radial distances (the ends) on the equatorial plane of rotation like the apple. This longitudinal spin axis may be putting the most surface mass furthest from the center of rotation (I'm not sure), or there may be other things going on...
    Last edited: Nov 10, 2012
  5. Nov 10, 2012 #4

    Simon Bridge

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    Eventually, sure. This is a discussion not a thesis. I'd prefer to see how OP understands things before writing a novel.

    Not in NZ they don't. Apples in NZ tend to roll in a circle due to being fatter at the stem end.

    pole-over-pole motion of the apple makes for more bouncing because the shape is most variable around that line. More bouncing means more likely to change the roll axis - means less stable. Have a go rolling some apples and see.

    apples are quite complicated shapes, and irregular, the point of watching the football roll was to get a feel for how a shape can contribute to a preferred stable roll axis (note "roll" is not "spin"). I did not mean anyone to think I was suggesting that a football rolls like an apple does. To understand complex shapes you must start with simpler ones.
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