The discussion focuses on determining the direction of friction acting on rolling objects, particularly in the context of a ball given a horizontal impulse. It is established that friction opposes the motion of the contact point of the object with the surface. For instance, when a car accelerates to the right, the friction force at the tires acts to the right to prevent slipping. Conversely, when decelerating, friction acts to the left. The conversation also highlights the importance of understanding the relationship between linear velocity and angular velocity in rolling motion, emphasizing that static friction ensures the point of contact remains stationary.
PREREQUISITESPhysics students, mechanical engineers, and anyone interested in the dynamics of rolling motion and frictional forces in real-world applications.
The constraint that static friction imposes is that the point on the ball that is in contact with the ground is instantaneously stationary, i.e., has v=0. As said above, the direction of the friction can be either way-- whatever is necessary to achieve v=0. Now this is not a simple constraint, because friction is a force, and v is a velocity, and force does not produce velocity it produces acceleration and torque. But the thing you can "take to the bank" is that the friction will produce a horizontal time dependent force, call it F(t), that is whatever is required to insure the point that touches the ground always has v=0. That constraint is made useful by connecting it to the speed of the ball V and the rotation rate of the ball W, which thus must have the simple connection V=R*W, if R is the radius of the ball. Then you look at whatever other forces are on the ball, and write the free-body diagram for the net force that controls V, and the net torque that controls W, and then F(t) will be whatever it takes to allow V=R*W to prevail at all times. So this will depend on what other forces are in play, and what torque they represent.david456103 said:
A ball given a sharp horizontal impulse will almost surely slide to begin with. The peak force during the impulse is likely to overcome static friction. As it slides, the dynamic friction applies a torque, accelerating the ball rotationally and slowing it linearly. When the rotation rate matches the linear speed (so that the point of contact is instantaneously stationary) rolling commences. At this point, there will be far less frictional force. Flexing in the surface tends to slow the ball down. Since that would cause the rotation to outstrip the linear motion, a static frictional force arises acting forwards on the ball. This slows the ball rotationally while helping to maintain its forward motion, keeping the two in synch.david456103 said:
In my opinion, the only way this is possible is if the ball is hit so high that it is initially spinning faster than it is rolling. If you add an impulse p to a ball at distance x from the center, the ball will have mv=p, and its angular momentum will be I*w = p*x. Thus v = p/m = I*w/(mx) = 2/5 R2*w/x. That will be less than R*w any time x > 2/5 R. So if you strike it more than 2/5 from its center, assuming the cue doesn't slip off, you can make it spin faster than it is translating, and so it will actually grab and speed up. Too bad you can't do it with conservation of energy-- while it is sliding it will be dissipating energy, so you have to solve for when v = w*R. But v will always exceed the initial value of x > 2/5 R, because the frictional force is forward. It's always kinetic friction too-- by the time static friction kicks in, the ball will roll with constant speed.david456103 said:
