If a spherical body is given some velocity and it then starts pure rolling on a plane surface(not inclined), will the body come to rest if we ignore other factors like surface irregularities and air resistance? Also how and which direction does static friction act in?
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In the absence of any external forces (notably air drag and rolling resistance) the body could theoretically roll at constant velocity forever per Newton’s first law. Under these conditions there would be no static friction involved (nor the need for it).
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Bob D
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If we ignore friction between the surface and the ball, it's hard to say that it's really rolling. We can arbitrarily give it an angular velocity such that the sum of tangent velocity and translational velocity is zero, but any other angular velocity would be just as good.
Once we let there be friction between the surface and the ball, it's contradictory to assume that there are truly no surface irregularities (as opposed to only very small ones), since microscopic surface irregularities are what gives us friction in the first place. However, it is reasonable to assume that the rolling friction that results from surface irregularities is very small and that the ball will roll for a very long time.
If we let there be friction between the surface and the ball, and we start the ball with zero angular velocity and some finite translational velocity with respect to the surface, the ball does not start to roll when it touches the surface. It starts to skid.
You can do this experiment. Visit a basketball or volleyball court, get yourself a nice hard ball, kneel down on the floor, and do your best, no-angular-velocity forward toss a couple of centimeters above the floor. Observe what happens as the ball comes into contact with the floor.
In the real world of objects that are not perfectly rigid, this skidding will irregularly deform both the surface and the ball such that when the surface rebounds to its equilibrium shape, part of the energy released will push them apart. There will be some combination of skidding and bouncing. If you've ever tried to push a rubber-footed chair or table across a smooth floor and heard the awful juddering sound that it makes, that's this effect in action.
If we work in an idealized world of near-perfect rigidity, and release the ball a negligible distance above the floor, we can ignore the bouncing and focus on the skidding.
The force of friction works opposite the direction of motion as usual. The force of kinetic friction between the surface and the ball transfers kinetic energy from the ball's translational kinetic energy to the ball's rotational kinetic energy. Some of the translational kinetic energy is also converted to heat in real life (with the above intermediate steps of bouncing and making juddering sounds).
Once enough of the translational kinetic energy has been transferred to rotational kinetic energy that the sum of tangent velocity (with respect to the center of the ball) and translational velocity (with respect to the floor) is zero at the interface between the ball and the floor, the ball is rolling and not skidding.
Once the ball is rolling and not skidding, kinetic friction is zero. Rolling friction is nonzero and points opposite the direction of movement, but it may be negligible over the time we are interested in. Static friction is also zero unless some force causes the ball to accelerate.
End-note: "Why zero kinetic friction? My physics textbook says..."
Normally when rolling is considered, especially in introductory physics, we start the ball and the surface stationary and then we accelerate the ball, for instance by releasing it at the top of an inclined plane. If the ball is accelerating without slipping, it must also be angularly accelerating. Static friction is the force which facilitates the transfer of energy from whatever energy reservoir is providing the acceleration (for instance, the gravitational field on a ball on an inclined plane) to or from the rotational kinetic energy of the ball$^1$.
Zero energy transfer over nonzero distance, as in the case of a ball rolling at constant velocity on a level plane, necessarily implies zero force.
- ...or the total energy of the system causally attached to the rolling of a wheel, like the powertrain of an automobile.
g s
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