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Homework Help: Linear velocity!

  1. May 24, 2014 #1
    1. The problem statement, all variables and given/known data

    What is the linear velocity of the foot if the angular velocity of the dynamometer was 180 degrees/s and the distance from the knee joint to the foot is 0.5 m. Give your answer rounded to two decimal places in m.s-1. (Do not include units in answer).

    2. Relevant equations

    linear velocity = angular velocity (w) x radius (r).
    linear velocity = w x r.

    3. The attempt at a solution

    w = 180 degree/s
    r = 0.5m
    linear velocity = ?

    linear velocity = w x r
    linear velocity = 180 x 0.5
    linear velocity = 90 degrees/s

    To find radians, 90/57.3 = 1.57 m/s

    Is this correct? And in the right units?

    Please help and thank you! :)
  2. jcsd
  3. May 24, 2014 #2


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    Well, your relevant equation gives ##0.5 {\rm m}\, \times \,\pi \, {\rm rad/s} = 1.57 \,{\rm m/s}## straightforward.

    But your dealing with units is a bit messy. Especially the 90 degrees/s is objectionable. A linear velocity has dimension length/time. The numerics are fine, but the dimensions should read something like: degrees/s / radians/degree x meters/radian

    THe writer of the exercise doesn't want to be bothered by these considerations, so he/she asks for a number only.

    In my first sentence I let the radians disappear, you could say that I cheat too. My defence is: radians is arc per radius, so length/length and thereby dimensionless: it can be skipped in dimensional expressions.
  4. May 24, 2014 #3
    Thank you so much! Great help :)
  5. May 24, 2014 #4
    It is easier to understand if you convert to radians first and then calculate the linear velocity.
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