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Fluster
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For an object sliding on a horizontal surface, there is a dive effect caused by friction. This means that the front edge of the object is "diving" towards the surface and the back edge has some lift. As a result the friction will be stronger in the front edge of the object, which typically explains curving motion of an object having spin around vertical axis - the front edge pushes the object in one direction stronger that the back end to the other direction.
For an object such as a cube I think this is easily explained. Friction doesn't work against the center of mass of the cube, but along its bottom side. Hence the friction attempts to accelerate a rotating motion on the cube, but due to the shape of the cube rotation would require either lift of its center of mass or the front edge burying in the surface. While the rotating force is not strong enough to do either, the surface answers the downward push with an equal lift force. Similarly in the back edge the rotating force resists gravitation and reduces the lift required by the surface to keep the object on it. With a crude simplification, the front half of the cube then faces friction force of (½m + x)g and the back half (½m - x)g where m is the total mass of the cube. As sliding continues, x will grow until eventually the back edge will rise from the surface and the cube flips on its other side.
To this point all is clear (assuming that I'm right). But here's the puzzle.
After watching some tutorial videos I have learned that this same effect seems to work with a billiard ball, and I can't figure it out. It seems to be a known fact that a ball with a vertical spin tends to curve while its sliding (I don't think its anymore possible in the rolling part of movement where the spin is fixed to the linear motion). Furthermore it is known than this effect can be greatly increased by hitting the ball with the stick in higher vertical angle. A horizontal hit may cause no curve at all, but a hit from say 30° the makes the curve significant. Sounds like a perfect example of creating a push against the surface.
The problem for me is here that my previous reasoning doesn't seem to work. The first observation is of course that the ball must bury to the surface for a bit to make the contact point circular instead of a point. But even then we still need the force pushing towards the front of the circle and lifting the back of it. While friction causes exactly the same rotational force as with the cube, in this case the rotational acceleration is not resisted by neither gravitation nor the surface. Instead the rotational force works along the perimeter of the ball and doesn't seem to generate any difference on the pressure between the front and back parts of the contact circle.
So how is this effect explained for a ball?
For an object such as a cube I think this is easily explained. Friction doesn't work against the center of mass of the cube, but along its bottom side. Hence the friction attempts to accelerate a rotating motion on the cube, but due to the shape of the cube rotation would require either lift of its center of mass or the front edge burying in the surface. While the rotating force is not strong enough to do either, the surface answers the downward push with an equal lift force. Similarly in the back edge the rotating force resists gravitation and reduces the lift required by the surface to keep the object on it. With a crude simplification, the front half of the cube then faces friction force of (½m + x)g and the back half (½m - x)g where m is the total mass of the cube. As sliding continues, x will grow until eventually the back edge will rise from the surface and the cube flips on its other side.
To this point all is clear (assuming that I'm right). But here's the puzzle.
After watching some tutorial videos I have learned that this same effect seems to work with a billiard ball, and I can't figure it out. It seems to be a known fact that a ball with a vertical spin tends to curve while its sliding (I don't think its anymore possible in the rolling part of movement where the spin is fixed to the linear motion). Furthermore it is known than this effect can be greatly increased by hitting the ball with the stick in higher vertical angle. A horizontal hit may cause no curve at all, but a hit from say 30° the makes the curve significant. Sounds like a perfect example of creating a push against the surface.
The problem for me is here that my previous reasoning doesn't seem to work. The first observation is of course that the ball must bury to the surface for a bit to make the contact point circular instead of a point. But even then we still need the force pushing towards the front of the circle and lifting the back of it. While friction causes exactly the same rotational force as with the cube, in this case the rotational acceleration is not resisted by neither gravitation nor the surface. Instead the rotational force works along the perimeter of the ball and doesn't seem to generate any difference on the pressure between the front and back parts of the contact circle.
So how is this effect explained for a ball?
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