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A ball is rolling freely on a flat surface

  1. Dec 7, 2009 #1
    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.
     
  2. jcsd
  3. Dec 7, 2009 #2

    mgb_phys

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    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
     
  4. Dec 7, 2009 #3
    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?
     
  5. Dec 7, 2009 #4

    mgb_phys

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    - at least in the world of physics homework, or cars driving on ice
     
    Last edited: Dec 7, 2009
  6. Dec 7, 2009 #5
    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?
     
  7. Dec 7, 2009 #6
    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.
     
  8. Dec 7, 2009 #7
    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?
     
  9. Dec 7, 2009 #8
    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.
     
  10. Dec 7, 2009 #9
    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
     
  11. Dec 7, 2009 #10
    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!

    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).
     
  12. Dec 7, 2009 #11

    russ_watters

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    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.
     
  13. Dec 7, 2009 #12

    mgb_phys

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    A ball which is already rolling should (IMHO) continue to roll on a friction free surface.
    It has angular momentum
     
  14. Dec 7, 2009 #13
    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?
     
  15. Dec 7, 2009 #14
    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!
     
  16. Dec 7, 2009 #15

    russ_watters

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    Yes - I wasn't correcting you, I was just saying that the answer is even more generic.
     
  17. Dec 7, 2009 #16

    russ_watters

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    I agree.
     
  18. Dec 7, 2009 #17
    Excellent, thank you all for your help.
     
  19. Dec 7, 2009 #18
    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.
     
  20. Dec 7, 2009 #19

    ideasrule

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    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.
     
  21. Dec 7, 2009 #20
    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 shouldnt 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.
     
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