# A ball is rolling freely on a flat surface

• donotremember
In summary, the correct answer for the first question is (b) and for the second question, the correct answer is (d). The reason is that on a flat surface with friction, the force of friction points in the direction of motion of the center of mass, and when a ball hits a patch of ice, it will continue to roll as before without any change in its rotational or translational motion. The statement that on a frictionless surface, "friction for uniform rolling is zero" is true, and this means that on a frictionless surface, the rotational and translational motion are independent and will continue at constant velocities.
donotremember
This is a concept question from a previous final physics exam.

The correct answer is (b) and my professor confirms this, but I can't understand why the answer is not (d) since the question seems to imply that the ball is already in rolling motion and that friction would not play a part.

A ball is rolling freely on a flat surface.

(a) The force of friction points opposite to the motion of the centre of mass.
(b) The force of friction points in the direction of motion of the centre of mass.
(c) The force of friction cannot be determined.
(d) The force of friction is zero.
(e) None of the above.

You throw a tennis ball of radius R on the floor such that it rolls freely on a flat surface
for some time and then it hits a patch of ice where the coefficient of friction between the
ball and the ice is s = 0. When the ball hits the patch

(a) It continues to roll as before.
(b) It starts to spin (omega > Vcm/R)
(c) It begins to skid (omega < Vcm/R)
(d) none of the above

The correct answer for this one is (c) but I can't understand why its not (a). This is likely due to the same error I am making in the first question.

It's impossible for a ball to roll on a friction free surface - it can only slide.
It's not very intuitive why this is true and confuses a lot of people.

You have to consider whare forces must be acting to cause something to roll.
A good way of think of a roll is - suppose you were doing a forward roll in gym, you have to push backward with your foot. If there was no friction between the florr and your sneaker you couldn't roll - you would only slide forward

So if a ball is rolling for some time on a surface with friction and moves onto a surface without friction it will stop rotating and only translate?

- at least in the world of physics homework, or cars driving on ice

Last edited:
This is a website where I have found an explanation of rolling motion:

http://cnx.org/content/m14384/latest/

On this site it says:

There is a surprising aspect of rolling motion on a surface (which is not friction-less) : “Friction for uniform rolling (i.e. at constant velocity) on a surface is zero”.

Is this statement false?

The correct interpretation on a frictionless horizontal surface is that the rotational and translational motion are independent, or not coupled by the radius r.

Thus the angular momentum is conserved and the translational momentum is conserved from the known initial conditions in accord with Newton's First law.

SystemTheory said:
The correct interpretation on a frictionless horizontal surface is that the rotational and translational motion are independent, or not coupled by the radius r.

Thus the angular momentum is conserved and the translational momentum is conserved from the known initial conditions in accord with Newton's First law.

Wouldn't that mean the answer to the question "So if a ball is rolling for some time on a surface with friction and moves onto a surface without friction it will stop rotating and only translate?" is 'no' since the ball will retain whatever translational and rotational motion it had just before going onto the frictionless surface?

Just for the record what do you consider to be the correct answers to the concept questions?

I'm considering your original questions while reading the reference you include. It appears from a related thread I must brush up on the dynamics of rotational motion.

Yes, a rolling body should continue to rotate at constant angular velocity when it hits the frictionless surface, and it should continue to move at constant linear velocity according to Newton's laws. It becomes like a body spinning and moving through space in one direction with no forces acting externally.

SystemTheory said:
I'm considering your original questions while reading the reference you include. It appears from a related thread I must brush up on the dynamics of rotational motion.

Yes, a rolling body should continue to rotate at constant angular velocity when it hits the frictionless surface, and it should continue to move at constant linear velocity according to Newton's laws. It becomes like a body spinning and moving through space in one direction with no forces acting externally.

This is my intuition as well but it comes into conflict with supposed answers to the concept questions if we are to take "A ball is rolling freely on a flat surface" and "throw a tennis ball ... rolls freely on a flat surface for some time" to mean rolling motion ie. constant linear and angular velocity with 0 linear and angular acceleration

donotremember said:
This is a concept question from a previous final physics exam.

You throw a tennis ball of radius R on the floor such that it rolls freely on a flat surface
for some time and then it hits a patch of ice where the coefficient of friction between the
ball and the ice is s = 0. When the ball hits the patch

(a) It continues to roll as before.
(b) It starts to spin (omega > Vcm/R)
(c) It begins to skid (omega < Vcm/R)
(d) none of the above

The correct answer for this one is (c) but I can't understand why its not (a). This is likely due to the same error I am making in the first question.

I think the person who wrote the question (maybe your professor) made a mistake. I would pick (d), because technically, the ball is no longer rolling but spinning freely in space, and I expect motion to remain omega = Vcm/R. The exact logic and terminology is tough here.

The common experience is when you hit a patch of ice in your car while applying the brakes. The car starts to skid right away, because the brakes are applied. I rode dirt bikes and drove aggressively in snow in my younger days, and you learn to use throttle and stearing in anticipation of a skid, and go easy on the brakes in low traction conditions. Same goes for riding a ten speed bike, and going off road to low traction conditions. Rather than hit the brakes and lose control, one learns to downshift, pedal harder, and stear away from danger!

donotremember said:
This is a concept question from a previous final physics exam.

The correct answer is (b) and my professor confirms this, but I can't understand why the answer is not (d) since the question seems to imply that the ball is already in rolling motion and that friction would not play a part.

A ball is rolling freely on a flat surface.

(a) The force of friction points opposite to the motion of the centre of mass.
(b) The force of friction points in the direction of motion of the centre of mass.
(c) The force of friction cannot be determined.
(d) The force of friction is zero.
(e) None of the above.

I would not guess (b) unless sliding friction is implied between the ball and the surface. This would reduce the rate of rotational and translational velocity, and cause the ball to come to a stop. However the stopping force must act in the other direction (the force the ground exerts on the ball must oppose the translational velocity to cause decelleration).

mgb_phys said:
It's impossible for a ball to roll on a friction free surface - it can only slide.
Even worse, if a ball is rolling at a constant speed, there is no frictional foce, regardless of if the surface is frictionless or not! So regardless of other factors, if the ball is moving at constant speed, the answer is D.

And just what does "rolling freely" mean anyway?

What a terrible question!

And the correct answer to the second question most certainly is a.

A ball which is already rolling should (IMHO) continue to roll on a friction free surface.
It has angular momentum

Therefore the consensus will be:

The correct answer to the first question is (d), NOT (b)

The correct answer to the second question is (a), NOT (c)

Do we all agree?

SystemTheory said:
The common experience is when you hit a patch of ice in your car while applying the brakes. The car starts to skid right away, because the brakes are applied. I rode dirt bikes and drove aggressively in snow in my younger days, and you learn to use throttle and stearing in anticipation of a skid, and go easy on the brakes in low traction conditions. Same goes for riding a ten speed bike, and going off road to low traction conditions. Rather than hit the brakes and lose control, one learns to downshift, pedal harder, and stear away from danger!

When I was a kid I used to drive my bike around on a frozen pond in the winter. The low coefficient of friction of ice makes turning very difficult!

mgb_phys said:
A ball which is already rolling should (IMHO) continue to roll on a friction free surface.
It has angular momentum
Yes - I wasn't correcting you, I was just saying that the answer is even more generic.

donotremember said:
Therefore the consensus will be:

The correct answer to the first question is (d), NOT (b)

The correct answer to the second question is (a), NOT (c)

Do we all agree?
I agree.

Excellent, thank you all for your help.

Those answers look reasonable to me although the concept of "rolling" on a frictionless surface is an oxymoron. A rolling body has coupled rotational and translational variables, as if radius r acts like a power transformer.

Bicycle is harder to stear on ice than a motorized vehicle in my experience.

Let's see. If a friction force of f is exerted on the ball's contact point with the ground, Newton's second law says the ball should slow down. However, if you analyze the torque about the contact point, you'll find that it's 0. Hence, the ball shouldn't slow down. I don't pretend to know the solution to this apparent paradox.

I have a problem with the answer that if the ball is in constant speed when it is rotating then the answer is D. But i have read that for a rotating motion, there is always an angular acceleration and for a accelerating body a force must be acting. so shouldn't there be any frictional force which is the reaction force of the force that makes the ball rotate. well i am just taking physics and i am not so good. just wanted to make sure.

Again, the answer for the question was given b by our professor also. because according to him ( as far as i remember bcoz it was a long time ago) the surface of the ball in contact with the ground is moving oppostive to the motion of CM of the ball. and for that motion, frictional force is required to act on the opposite side. that implies that the frictional force is in the direction of the center of mass. this is what i am thinking for the case of cars and buses till now. am i on track?? please correct me if i am wrong.

SystemTheory said:
Those answers look reasonable to me although the concept of "rolling" on a frictionless surface is an oxymoron. A rolling body has coupled rotational and translational variables, as if radius r acts like a power transformer.
True. What would really be happening is that the object would be rotating at a speed that happens to equal the speed of translation. It would neither be rolling nor sliding.

mikhailpavel said:
I have a problem with the answer that if the ball is in constant speed when it is rotating then the answer is D. But i have read that for a rotating motion, there is always an angular acceleration and for a accelerating body a force must be acting. so shouldn't there be any frictional force which is the reaction force of the force that makes the ball rotate. well i am just taking physics and i am not so good. just wanted to make sure.
No. For a rotating body, the acceleration force at a point on the perimeter is perpendicular to the direction of motion. It is an entirely internal force and has no implications on this problem or conservation of energy.

donotremember said:
A ball is rolling freely on a flat surface. ... friction
As pointed out already, if the ball is rolling 'freely', then there is no friction force. If there is aerodynamic drag but no rolling resistance, then the friction force is in the direction of travel. If there is rolling resistance and no aerodynamic drag, then the friction force opposes the direction of travel (otherwise the ball wouldn't decelerate), while also applying an opposing torque to the ball's angular momentum.

ideasrule said:
Let's see. If a friction force of f is exerted on the ball's contact point with the ground, Newton's second law says the ball should slow down. However, if you analyze the torque about the contact point, you'll find that it's 0. Hence, the ball shouldn't slow down. I don't pretend to know the solution to this apparent paradox.
Consider a wheel speeding through space with no rotational motion. It just has linear velocity. Now the tip touches a frictional surface, friction acts backward accelerating the rotational motion and decelerating the linear motion. Since you consider the contact point as the reference, torque due to friction is zero. If you compute the angular momentum w.r.t contact point at any point during the force's action or after the wheel attains uniform rolling, you will see that angular momentum hasn't changed. This is because though linear velocity decreases, angular velocity and rpm (w.r.t com of the wheel) increases to compensate for it keeping the angular momentum w.r.t contact point constant.

I've rephrased the question and include my sketch.

A ball rolls on a horizontal surface with constant velocity at the center of mass given by Vcm. In which direction does the ball exert a force on the surface?

The sketch shows this as the action force $$F_{A}$$ that the ball exerts on the surface. It shows friction as the reaction force $$F_{R}$$ that the surface exerts on the ball. When the ball rolls in otherwise ideal surroundings the net force is zero but the motion is coupled by static friction at the rolling point. When it moves on a frictionless surface there is no rolling point and two kinds of motion can become independently defined.

PS - Anyone know how to insert an image with the text? I like when its done, but don't know how to do it.

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sganesh88 said:
Consider a wheel speeding through space with no rotational motion. It just has linear velocity. Now the tip touches a frictional surface, friction acts backward accelerating the rotational motion and decelerating the linear motion.
The math for this was covered in this thread:

Jeff Reid said:
The math for this was covered in this thread:

No. ideasrule doubted how the wheel's speed could change when the torque about the contact point is zero. That thread considers torque about COM of the sphere.

sganesh88 said:
No. ideasrule doubted how the wheel's speed could change when the torque about the contact point is zero. That thread considers torque about COM of the sphere.
If frame of reference is the contact point, the reaction force to deceleration acts at the COM, and that would generate a torque.

Jeff Reid said:
If frame of reference is the contact point, the reaction force to deceleration acts at the COM, and that would generate a torque.
No he wasn't talking about frame of reference. The contact point was the reference point for computing torque and angular momentum. Frame is the usual inertial ground surface..

sganesh88 said:
This is because though linear velocity decreases, angular velocity and rpm (w.r.t com of the wheel) increases to compensate for it keeping the angular momentum w.r.t contact point constant.

Let's consider a ball that has started rolling and is continuing to roll. Is linear velocity decreasing? If angular momentum wrt to the COM stays the same, the ball's rate of rotation omega stays the same. Since v=omega*r, linear velocity must also remain the same.

If angular momentum wrt to the COM stays the same, the ball's rate of rotation omega stays the same. Since v=omega*r, linear velocity must also remain the same.
If angular momentum wrt to the COM stays the same, the ball's rate of rotation omega stays the same and if the ball is rolling uniformly, i.e., if v=r*omega throughout its motion-this we cannot take for granted- , then yes, the linear velocity remains the same.

donotremember said:
Therefore the consensus will be:

The correct answer to the first question is (d), NOT (b)

The correct answer to the second question is (a), NOT (c)

Do we all agree?

I would agree with this. Professors...I've seen a lot of professors be outright wrong in my days. It's a very frustrating situation, because the professor and class end up laughing at YOU, because, after all, how can the professor be wrong?

One professor made the claim that to go fast doesn't require power...just gearing (I'm talking on the Earth in the real world). When I brought up the question of why an aircraft carrier needs a million horsepower, his answer was that acceleration needs power, and an aircraft carrier needs to constantly accelerate to point itself towards the wind.

I was like...ooh.

k.

And yes, he confirmed that the USS Nimitz can go 30 knots through the Atlantic using only a small electric motor and the right gearing :P

Plently of other examples in my college days...

## 1. What is the force that causes a ball to roll freely on a flat surface?

The force that causes a ball to roll freely on a flat surface is gravity. The weight of the ball creates a force that pulls it towards the ground, causing it to roll.

## 2. How does the mass of the ball affect its rolling speed?

The mass of the ball does not affect its rolling speed. In the absence of external forces, all objects will fall at the same rate regardless of their mass. Therefore, a heavier ball will not roll faster than a lighter ball on a flat surface.

## 3. What factors affect the distance a ball will roll on a flat surface?

The distance a ball will roll on a flat surface is affected by the initial velocity of the ball, the angle at which it is released, and the surface friction. Other factors such as air resistance and the shape of the ball can also play a role.

## 4. Can a ball continue rolling indefinitely on a flat surface?

No, a ball cannot continue rolling indefinitely on a flat surface. Eventually, the ball will lose its kinetic energy due to friction and come to a stop. However, on a perfectly smooth and frictionless surface, the ball could theoretically continue rolling forever.

## 5. How does the surface material affect the rolling of a ball?

The surface material can affect the rolling of a ball by changing the amount of friction between the ball and the surface. A smoother surface with less friction will allow the ball to roll further, while a rougher surface with more friction will cause the ball to roll a shorter distance.

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