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Circular motion, static friction

  1. Jan 15, 2008 #1
    [SOLVED] Circular motion, static friction

    1. The problem statement, all variables and given/known data
    Hey, this is more of a concept question than a homework question, but here goes: If a ball is spun fast enough to move around the inside of a vertical cylinder at a roughly constant velocity for a few seconds without spiraling down the cylinder, what forces are acting on the ball?


    2. Relevant equations



    3. The attempt at a solution
    I think the centripetal acceleration is provided by a normal force from the cylinder on the ball. Static friction must be preventing the ball from "falling" (that is, static friction cancels out the weight of the ball). I'm unsure about the "tangential" forces- I know the ball moves around the cylinder due to static friction, but I am unsure what force causes the ball to slow down... Is it rolling friction? Is there any occurance of kinetic friction in this situation? Thanks for any help.
     
  2. jcsd
  3. Jan 15, 2008 #2
    The faster it rotates the stronger the centripetal force and thus the stronger the normal force, increasing the force of friction in general(I think you got that much)

    Force is a vector, remember. In the down direction the force of gravity is unable to overcome the static friction, like you thought, in the tangential direction there's kinetic friction causing it to slow down, as it slows down, the centripetal and normal force decrease until gravity can start it moving down
     
  4. Jan 15, 2008 #3
    So kinetic friction can slow down a rolling object? This seems kind of counter-intuitive.
     
  5. Jan 15, 2008 #4
    Well strictly speaking, if it's perfect rolling motion(so no rolling AND translating, all rolling, which requires just the absolute right force of friction at the point of contact)then no energy is lost to friction

    If there's not enough friction the wheel or ball or whatever will slip and have that "spin in place" type of effect, if there's too much it'll slide without rolling right, but in ideal perfect rolling motion no, it'll go forever

    But from life experience, how many times have you seen something roll forever? So when they say ideal they do mean ideal
     
  6. Jan 15, 2008 #5
    well obviously I've never seen something roll forever, but I've never seen something roll in a vacuum. I know air resistance will slow down any moving object, but I also agree that it would be near impossible to perfectly spin an object so it rolls without kinetic friction. My problem I guess is how do I know if the question is assuming this ideal situation or not? We make simplifying assumptions all the time with physics problems (rigid bodies, particle modeling, etc.) I'll try the problem I'm stuck on, this time including kinetic friction and I'll let you know how it goes.

    Thanks for your help, it's been much appreciated!
     
  7. Jan 15, 2008 #6
    the force of friction is opposing the translational motion down the cyclinder (caused by gravity), not so much the translational motion caused by the ball rolling around the cyclinder.

    the forces of concern here are the force of gravity (down), the normal force (radial, and cause of centripital acceration) and the force of friction (up, proportional to the normal force), which govern if the ball holds up in the cylinder or how fast the ball will slide down the cylinder.
     
  8. Jan 15, 2008 #7
    True enough, but if in a problem they tell you the angular velocity is constant, there has to be a pretty sizable force counteracting the tangential static friction force. I'm assuming this is kinetic friction, but is this a safe assumption?
     
  9. Jan 15, 2008 #8
    Also, the static friction pointing up is equal to the weight; it's proportionality to the normal force is irrelevant, since I'm assuming the ball doesn't spiral down.
     
  10. Jan 15, 2008 #9
    Well if you're assuming that then yes

    If angular velocity is constant, there's no angular acceleration, and no torque, which is fine, it shouldn't accelerate. The way you say the problem it sounds like there's nothing actively driving it, you get it going then let go and let it do whatever and watch, so yes, angular velocity shouldn't increase any more than something sliding over a frictionless surface with no other forces acting should acclerate

    EDIT: The first line is to your most recent post, the big paragraph is to your one before that
     
    Last edited: Jan 15, 2008
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