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david456103
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I am really confused as to how to determine the direction of friction acting on a rolling object. Could someone help clarify how to determine the direction of friction? ANy help is appreciated ;)
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:let's consider the problem when a ball initially at rest on a surface with friction is given a horizontal impulse. According to some online sources, the ball will eventually attain a maximum speed after it is given the impulse. However, this makes absolutely no sense to me; isn't the friction opposing the motion, causing the velocity to strictly decrease?
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:let's consider the problem when a ball initially at rest on a surface with friction is given a horizontal impulse. According to some online sources, the ball will eventually attain a maximum speed after it is given the impulse. However, this makes absolutely no sense to me; isn't the friction opposing the motion, causing the velocity to strictly decrease?
According to some online sources, the ball will eventually attain a maximum speed after it is given the impulse...
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:The ball leaves the cue with a given speed v0 and an unknown angular velocity ω0. Because of its initial rotation, the ball eventually acquires a maximum speed of (9/7)v0(?). Find h/R.
The given solution uses angular momentum, which completely makes sense to me, but this problem does not make any conceptual sense to me. How can the ball increase in translational speed when there is friction?
The direction of friction in rolling motion is opposite to the direction of motion of the rolling object. This means that the frictional force acts in the opposite direction to the rolling motion, slowing down the object.
This is because of the point of contact between the rolling object and the surface. The point of contact is stationary, thus the frictional force acts in the opposite direction to the motion of the object.
The direction of friction plays a crucial role in the motion of a rolling object. It creates a torque, causing the object to rotate and slowing down its forward motion. This is why rolling objects eventually come to a stop, unlike sliding objects which experience a constant frictional force.
Yes, the direction of friction can change depending on the surface the object is rolling on. For example, if the surface is soft or uneven, the direction of friction may change due to the changing points of contact. Additionally, if the object is rolling uphill or downhill, the direction of friction may also change.
The direction of friction affects the energy of a rolling object by converting some of its kinetic energy into heat. This is because friction is a non-conservative force, meaning it dissipates energy rather than conserving it. Thus, the direction of friction ultimately leads to a decrease in the object's overall energy and speed.