# Slipping vs No Slipping Ball Race

• ColinD
In summary: No idea what "on its own" means, but acceleration depends on the net force, which includes all forces, including static friction.In summary, static friction does not cause an acceleration on its own though? Static friction does not cause an acceleration on its own though? static friction does not cause an acceleration on its own though?No idea what "on its own" means, but acceleration depends on the net force, which includes all forces, including static friction.
ColinD
The setup is a flat friction surface where the ball rolls without slipping. Next, in one case it goes up a friction incline, and in the other a frictionless incline. Which ball leaves the incline faster? Both are given the same initial push.
At the bottom of the incline both balls have the same energy and are rolling w.o slipping. But in the frictionless case the ball keeps spinning just as quickly as there is no torque. However, its center of mass slows down from gravity. In the friction case, does friction cause a torque? If so, then the center of mass slows down more. But if not, then gravity slows the balls center of mass velocity down just as much, and this acceleration from gravity also (because v=wr) slows the spinning down too. So it seems even if friction on the ramp doesn't slow the ball down, it ends with less energy.

When I say which leaves faster, I mean which has greater center of mass velocity. Does friction on the ramp slow the center of mass velocity down? If not then both cases the center of mass is only accelerated by gravity so they end with the same final velocity, but one is spinning slower so their energies are different. Oh, I guess this means their final heights are different, the frictionless ramp ball must have a lower hieght as its rotational energy is greater and translation energy is the same. That is, if static friction on the ramp doesn't slow the center of mass velocity.

I guess that's the main dilemma my problem comes down to. I remember that any force applied anywhere accelerates the center of mass as if it were applied to the center of mass, so I feel like friciton should slow transnational velocity, yet I've read that it doesn't. Please tell me what is wrong with that statement. I know there are other arguments like there is no displacement so no work, I get why those are right, but I don't understand why the statement "any force applied anywhere accelerates the center of mass as if it were applied to the center of mass, so friciton should slow transnational velocity" is incorrect.

Thank you for any insight.

ColinD said:
In the friction case, does friction cause a torque? If so, then the center of mass slows down more.
Be careful here. Think about the direction of the force and the torque and how the angular momentum will change.

ColinD said:
their energies are different.
If there is only static friction (no dissipative losses), their total energies (PE + KElinear + KErotiational) are the same and constant over time.

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So the maximum height it reaches in the frictionless case is less, which is strange because both cases have the same initial center of mass velocity and experience identical center of mass acceleration (only due to gravity, not friction), yet the center of mass behaves differently. How?

ColinD said:
identical center of mass acceleration (only due to gravity, not friction)
Acceleration is a function of the sum of all forces, including static friction.

Static friction does not cause an acceleration on its own thought, correct? I am talking in the ideal case with no deformation. If a ball was rolling without slipping on a flat surface it wouldn't slow down, it would roll forever. Isnt it the same going up an incline?

ColinD said:
Static friction does not cause an acceleration on its own thought, correct?
No idea what "on its own thought" means, but acceleration depends on the net force, which includes all forces, including static friction.

ColinD said:
Im talking in the ideal case with no deformation. If a ball was rolling without slipping on a flat surface it wouldn't slow down, it would roll forever. Isnt it the same going up an incline?
When PE increases, what does it mean for KE?

That seems contradictory. How come in one case you take static friction does into account as a force, thus acceleration. But in the other the same force does not cause acceleration.

ColinD said:
That seems contradictory. How come in one case you take static friction does into account as a force, thus acceleration. But in the other the same force does not cause acceleration.
What is the static friction for a ball rolling on a plane without resistance?

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@ColinD which direction does the static friction point as the ball rolls up the hill, and how did you determine the direction?

It points down the hill. Its counterintuitive how static friction does zero work because there is no displacement of contact point, yet is changes the speed of the rolling ball.

ColinD said:
It points down the hill.
This is the problem in your reasoning. The static friction in this case actually points up the hill.

Can you figure out why?

ColinD said:
Its counterintuitive how static friction does zero work because there is no displacement of contact point, yet is changes the speed of the rolling ball.
Yes, this is counterintuitive

Counterintuitive? Yes and no!

There is a rough parallel with someone running up these two slopes. With no friction, the runner could do no better than slide to a halt, With friction, she could run up the slope.

The ball can't generate power as such, but the ball rolling into the slope is similar to the propulsion mechanism of a runner. (Push backwards - downhill - and get friction to drive you forwards - uphill.) With friction, therefore, the ball can sacrifice its rotational energy in order to get higher up the slope.

Dale
ColinD said:
It points down the hill.
No.

ColinD said:
Its counterintuitive how static friction does zero work because there is no displacement of contact point, yet is changes the speed of the rolling ball.
Work is frame dependent while the force is the same in all frames. In some other inertial frame the work might be negative or positive, but the acceleration still the same.

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## 1. What is the difference between slipping and no slipping in a ball race?

Slipping and no slipping refer to the movement of a ball in a race or track. In slipping, the ball is moving while also experiencing some friction or resistance, resulting in a loss of energy. In no slipping, the ball is moving without any friction or resistance, allowing it to maintain its speed and energy.

## 2. How does friction affect the movement of a ball in a race?

Friction is a force that opposes the movement of an object. In a ball race, friction can cause the ball to slow down or even stop if it is not powerful enough to overcome the force. This can result in slipping, where the ball is still moving but losing energy due to the resistance from friction.

## 3. Can a ball race have both slipping and no slipping movements?

Yes, a ball race can have both slipping and no slipping movements. This can happen if the ball experiences different levels of friction at different points in the race. For example, the ball may start off slipping due to high friction at the starting point, but then transition to no slipping as it reaches a smoother part of the track.

## 4. How does the surface of the ball and the race track affect slipping and no slipping?

The surface of the ball and the race track can greatly impact slipping and no slipping movements. If the ball has a rough surface, it may experience more friction and be more likely to slip. On the other hand, a smooth surface on both the ball and the track can reduce friction and allow for a no slipping movement.

## 5. Are there any real-life applications of studying slipping vs no slipping in a ball race?

Yes, understanding the dynamics of slipping and no slipping in a ball race has real-life applications, particularly in the fields of engineering and sports. For example, engineers may use this knowledge to design more efficient machines or vehicles, while athletes can use it to improve their performance in sports that involve balls, such as bowling or pool.

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