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How To Find Initial Angular Velocity

  1. Jun 7, 2015 #1
    1. The problem statement, all variables and given/known data
    The angle of a pendulum is θ(t)=(0.270rad)cos(4.00t+1.00π), where t is in seconds.
    Determine the initial angular velocity.

    2. Relevant equations


    3. The attempt at a solution

    I solved for the frequency, which was 6.37E-1 Hz and subbed it into the formula above and got 4rad/s which is the same ω in the equation but it is wrong. Am I missing something because I can't figure out what is wrong with my method.
  2. jcsd
  3. Jun 7, 2015 #2


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    The formula ω=2πf is not applicable to this case. That formula is for uniform circular motion, which has constant angular velocity, not for a pendulum, which has variable angular velocity.

    From the formula for θ you can deduce that initially (at time t=0) the pendulum is at its highest point, and hence at zero angular velocity.
  4. Jun 7, 2015 #3
    Ah okay, thanks!

    Did you just sub in 0 for t which gave you -0.270 at the θ to figure out that it was at its highest point?
  5. Jun 7, 2015 #4


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    Essentially yes. Cos attains its maximum absolute value at integer multiples of pi.
  6. Jun 7, 2015 #5
    Makes sense, thank you!
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