1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Rolling balls angular rotation

  1. Apr 17, 2010 #1
    If a cylinder is rolling without slipping, C is the centre of zero velocity for a moment and O is the centre

    Does the angular rotation about O equal to the angular rotation about C, or is there only one angular rotation when a cylinder is rolling, that is the rotation about the point of contact?

    3. The attempt at a solution

    This is a question that came to me, not a assignment question or anything, but anyway

    I think in the ordinary frame of reference a rolling cylinder only has an angular rotation about the point of contact, not about the centre

    Where in a frame of reference where you are following the cylinder, you should see the cylinder rotating about the centre and the surface is moving linearly without sliding.

    I know angular rotation is always about an a line, so a single motion can have many angular velocities with respect to many axis's.

    Is it possible to evaluate the angular velocity with respect to O in the normal frame of reference when the ground is stationary?

    i am not really sure i guess the angular velocity for each point on the shape would vary if you measure it from O since the whole object is kind of translating... and since C has a zero velocity
  2. jcsd
  3. Apr 18, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi SpartanG345! :smile:

    (btw, better to say "instant" rather than "moment", so as not to confuse with other types of moment :wink:)

    Angular velocity (unlike angular momentum) is the same about any point.

    Angular velocity is a "free" vector (strictly, a "free" pseudovector), so (unlike force) it has a direction, but not a specific line in that direction.

    Changing to a different inertial frame will, of course, alter the velocity, but will not alter the angular velocity.

    Formulas that combine I and ω use the same ω, no matter whether I (the moment of inertia) is about the centre of rotation or the centre of mass (btw, they don't generally work about any other point).
    Yes, you get τ = IOω, instead of 0 = ICω - rmv, which is the same since IC = IO + mr2.

    (I've used your notation, but usually we use C for centre of mass, and O for centre of rotation :wink:)
  4. Apr 18, 2010 #3

    Doc Al

    User Avatar

    Staff: Mentor

    Just to add to what tiny-tim has already explained...
    Since the cylinder rolls without slipping, its instantaneous axis of pure rotation is the point of contact. So you can describe the motion in two ways:
    (1) As a pure rotation about the point of contact.
    (2) As a combination of rotation about the center of mass plus translation of the center of mass.

    (Same ω in both cases, of course.)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook