Can a ball roll down a frictionless plane?

  • #1
I have posted this question before but have not got a complete answer. I have since been thinking about it quite often, yet still have not had a conclusive answer. I'd really appreciate if someone can give a full explanation, since it is a fact known by most.

1. Under all ordinary conditions, would a ball released from rest start rolling down a frictionless inclined plane with just the force of gravity pulling it down? Or is it really just going to slide down?

2. Now let's suppose a gigantic ball released on the slope of an enormous frictionless inclined plane, so that the gravitational force varies considerably from the bottom to the top of the ball? What would happen? Would the ball then start rolling?
 

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  • #2
Doc Al
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I have posted this question before but have not got a complete answer. I have since been thinking about it quite often, yet still have not had a conclusive answer. I'd really appreciate if someone can give a full explanation, since it is a fact known by most.
I'm afraid you're going to get the same answer.

1. Under all ordinary conditions, would a ball released from rest start rolling down a frictionless inclined plane with just the force of gravity pulling it down? Or is it really just going to slide down?
Do you understand that friction is required to get the ball rolling? And that gravity does not exert a torque on the ball.

2. Now let's suppose a gigantic ball released on the slope of an enormous frictionless inclined plane, so that the gravitational force varies considerably from the bottom to the top of the ball? What would happen? Would the ball then start rolling?
Why would you think a changing gravitational force matters?

Rather than just seek an answer, why don't you explain what you think is going on?
 
  • #3
I think that gravity does exert a net torque on the ball. I think that normal force acts at angle on the ball, and thus will cancel out some of the gravitational forces on the ball. The front of the ball then gets more torque than the back of it.
 

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  • #4
Doc Al
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I think that gravity does exert a net torque on the ball. I think that normal force acts at angle on the ball, and thus will cancel out some of the gravitational forces on the ball. The front of the ball then gets more torque than the back of it.
Gravity acts at the center of mass of the ball, thus it exerts no torque on it. And the line of action of the normal force goes through the center of the ball, thus it exerts no torque either.

The normal force does "cancel out" some of the gravitational force: The net force on the ball is less than its weight. (The net force will be mg sinθ down the incline.) But it doesn't produce a torque about the center of mass, which is what is required to get the ball to roll instead of just slide.
 
  • #5
ok. Yeah, I guess that makes sense. I drew a diagram and the force vectors again; they agreed with this idea. Thanks.
 
  • #6
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Gravity acts at the center of mass of the ball, thus it exerts no torque on it.
If the ball is on an inclined plane relative to gravity, the force on the center of mass does not pass through the point of contact with the plane. Therefore, I think you are incorrect that there is no torque on the ball.

Regards,

Bill
 
  • #7
If the ball is on an inclined plane relative to gravity, the force on the center of mass does not pass through the point of contact with the plane. Therefore, I think you are incorrect that there is no torque on the ball.
The gravitational force on the center of mass indeed does not pass through the point of contact, but that does that produce a net torque on the ball. The normal force on the ball acts through the center of mass and therefore affect the ball uniformly. The net force on the ball drags it down the plane.
 
  • #8
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Anyone who's ever gone bowling shouldn't have much trouble visualizing this one.
 
  • #9
Doc Al
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If the ball is on an inclined plane relative to gravity, the force on the center of mass does not pass through the point of contact with the plane. Therefore, I think you are incorrect that there is no torque on the ball.
Careful: Yes, there's a torque about the point of contact, but that point is accelerating, so it's not true that the rate of change of angular momentum about that point is given by the net torque about that point. (It turns out that it's zero.)

It's simpler to analyze the motion with respect to the ball's center of mass, where such complications do not arise. There's no torque about the center of mass, thus no change in rotation.
 
  • #10
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It is the friction that causes the ball to roll. So, without friction the ball would only slide without rolling. To give an example, if we had an artificial waterfal with an angle "alfa", and we have put a beach ball on it, and if we have released; then we would observe that, as the water is flowing down, (if the water is pressured down or much much water then of course the ball will roll.)the ball is sliding down and not rolling. Because the water creates artificially a frictionless surface for the ball.

____o___
---------\ This is the waterfall :)
----------\
-----------\
This can be observed under certain circumstances.
 
  • #11
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In order to solve for the bigger ball, try drawing a picture.
1. Take the center of mass as the pivot because this what a rolling ball rotates around; assuming the ball is uniform, it would be at the center of the sphere.
2. Draw in the action of gravitational force, even if the ball big enough that gravity varies significantly, it only varies with the vertical, and gravity acts straight down, meaning it acts through the center of mass, which is the pivot. Even if the center of gravity is different from the center of mass, gravity still acts straight down through the ball, acting thought the pivot point (the COM) and providing no torque
3. Draw in the Normal force, which acts normal to the plane. This too passes through the pivot point and provides no net torque.

No torque=no rolling

If you chose a different pivot point, the laws of physics would still be the same, so you would get the same final answer (the ball does not roll). Another pivot would result in torques that either cancel each other out coming from Gravity and the normal force or show rotational motion about a point that is represented exclusively by the linear motion of the ball.

Also, a changing force of gravity would only be relevant if it changed horizontally, because that would change where gravity acts and cause it to no longer act through the center of mass. That change would cause the ball to roll.
 
  • #12
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Would it be correct to say that as the ball is moving down a frictionless inclined plane, say, to the left, that a force is exerted on the inclined plane towards the right?
 
  • #13
Doc Al
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Would it be correct to say that as the ball is moving down a frictionless inclined plane, say, to the left, that a force is exerted on the inclined plane towards the right?
Sure. The incline plane and ball exert forces on each other perpendicular to the plane. (The "normal" force.) So if the ball slides down and to the left, the plane exerts a normal force up and to the left on the ball, and the ball exerts an equal normal force down and to the right on the plane.
 
  • #14
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With just that small amount of friction, the ball rolls slowly down the hill. If the ball is made out of lead, and the hill is teflon, will that small amount of friction cause static electricity? and which one would be positive and negative?


whats the best material for the ball and hill? to try to make static, but yet still have the ball roll some.....?
 
  • #15
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Is there even such a thing as a frictionless plane? Seems impossible to me.
 
  • #16
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There is no such thing as a completely frictionless plane; it's an idealization used to discuss the laws of physics while ignoring friction. The question is really more like, can gravity and the normal force torque a sphere? The closest we can get is in examples like the waterfall mentioned above.
 
  • #17
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oh. What kind of ball should I use? and surface?
 

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