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!

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: Dec 1, 2017
  2. jcsd
  3. Dec 1, 2017 #2

    kuruman

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, you can do that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted