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Velocity of an Object in Uniform Circular Motion

  1. Oct 5, 2014 #1
    1. The problem statement, all variables and given/known data
    An object of mass 0.5 kg is swung in uniform circular motion. The radius is 2 meters, and the force exerted is 4 N. Calculate the magnitude of the velocity.

    Answer Choices:
    a) 0.25 m/s
    b) 1 m/s
    c) 4 m/s
    d) 16 m/s

    2. Relevant equations
    v = 2piR/T
    F = mv^2/R

    3. The attempt at a solution
    Since I didn't know the variable time, I couldn't use the velocity equation. Next, I tried plugging in the variables for the centripetal force equation and solving for velocity:

    4 = (0.5)v^2/2
    4 = 0.5/2 + v^2/2
    4 = 0.3 + v^2/2 <- 0.3 because of significant figures
    (subtracted 0.3 from both sides)
    4 = v^2/2 <- 4 because of significant figures
    (multiplied both sides by 2)
    8 = v ^2
    (took the square root of both sides)
    v = 3 which isn't one of my answer choices.

    Maybe I'm not doing my algebra correctly or maybe I'm not using the right equation, but I couldn't find another equation using the variables I have. If I knew the time it took for one revolution I could use the velocity equation, but I don't know how to find time and I couldn't find an equation for finding it.
  2. jcsd
  3. Oct 5, 2014 #2
    There is an algebra mistake in going from the first to the second step. You have essentially turned a product into a sum instead.

    On a side note, when taking significant figures into account, do so only on the final answer. If you keep rounding off at each step, you will find that the rounding-off error grows substantially larger after each step, and the final answer you obtain might be significantly off the correct one.
  4. Oct 5, 2014 #3
    Ohh, okay, that makes a lot more sense. I'll be sure to keep that in mind about significant figures in the future, too.

    Thanks a lot!
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