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Homework Help: Angular velocity and friction

  1. Dec 1, 2017 #1
    1. The problem statement, all variables and given/known data

    A coin stands vertically on a table. It is projected forward (in the plane of itself) with speed v and angular speed w. The coefficient of kinetic friction between the coin and the table is u. What should v and w be so that the coin comes to rest (both translationally and rotationally) a distance d from where it started.

    2. Relevant equations

    I = 1/2mr^2

    T = r x f

    Ff = uFn

    F = ma

    T = Iw’

    3. The attempt at a solution

    For v:

    Ff = uFn

    Ff = umg

    Fnet = umg

    ma = umg

    a = ug

    v - ug(t) = 0

    v - ug(d/v) = 0

    v = (ugd)/v

    v^2 = ugd

    v = sqrt(ugd)

    For w:

    T = r x f

    T = umgr

    T = Iw’

    umgr = 1/2mr^2w’

    w’ = 2ug/r

    w - (2ug/r)(t) = 0

    w = (2ug/r)(d/v)

    w = (2ug/r)(d/(sqrt(ugd)))

    w = 2sqrt(ugd)/r
     
    Last edited by a moderator: Dec 1, 2017
  2. jcsd
  3. Dec 1, 2017 #2

    kuruman

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    Here you use t for "time" while later you use the same symbol for "torque". That could be confusing. Setting that aside, t for time cannot be replaced by d/v because the coin does not cover equal distances in equal times.
     
  4. Dec 1, 2017 #3
    I replaced the t’s that were used to represent torque with T.

    Can I replace t with 2d/v?

    d = avg velocity (t)

    t = d/(avg velocity)

    And average velocity is (vi + vf)/2 = (v +0)/2

    t = d/(.5v) = 2d/v
     
  5. Dec 1, 2017 #4

    kuruman

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    Yes, you can do that.
     
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