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Frame of reference of bicycle rider

  1. May 3, 2015 #1
    1. The problem statement, all variables and given/known data
    A wheel of a bicycle weighs 1 kg, all of which is at the rim. The diameter of the wheel is 0.7 m. If the bicycle is ridden at the speed of 3.5 m s–1, then in the frame of
    reference of the rider:

    i) Calculate the angular speed ω of the wheel.

    ii) Calculate the momentum of the rim, p.

    iii) Calculate the angular momentum of the wheel.

    iv) Calculate the kinetic energy of the wheel.

    2. Relevant equations

    ## v = {\omega} r ##
    ## \rho = mv ##
    ## L=I\omega ##
    ## Kinetic\ Energy = \frac{1}{2} m v^2 + \frac{1}{2} I \omega ^2##

    Moment of Inertia of a hoop (for the wheel, ignoring the spokes):

    ## I=M R^2 ##

    3. The attempt at a solution

    i) ## \frac {v}{r} = 10\ rad\ s^{-1}##

    ii) ## 0 \ {kg}\ m\ s^{-1}## (Since in the frame of reference of the rider, there is no linear translation?)

    iii) ## L=(M R^2) \omega ##
    ##(1) (0.35)^2 (10) = 1.225 {kg}\ m^2 ##

    iv) ##Kinetic\ Energy = \frac{1}{2} I \omega ^2## Ignoring the linear term again.

    ##Kinetic\ Energy = (0.5) (0.35) ^2 (10)^2 = 6.125 J ##

    Is this correct?

    Thank you.
     
    Last edited: May 3, 2015
  2. jcsd
  3. May 3, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Looks right.
     
  4. May 3, 2015 #3
    Thank you!
     
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