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Angular Displacement Differentiation

  1. Jun 7, 2012 #1
    1. The problem statement, all variables and given/known data
    An angular displacement θ radians in time t seconds is given by the equation θ = sin 3t. Find

    a:) angular velocity when t = 1 second
    b:) the smallest positive value of t for which the angular velocity is 2rad/s
    c:) the angular acceleration when t = 0.5 seconds
    d:) the smallest positive value of t for which the angular acceleration is 9rad/s


    2. Relevant equations
    d/dx (sin ax) = a cos ax
    d/dx (cos ax) = -a sin ax


    3. The attempt at a solution
    Ok i have worked out parts a:) and c:)

    a:) dθ/dt = 3cos 3t so when t = 1, ω = -2.97r/s

    c:) dω/dt = -9sin 3t so when t = 0.5, angular acceleration = -8.98r/s/s

    I can't work out parts b and d, its not a homework question i am revising from a book and the answers for parts b and d are 0.280seconds and 1.57 seconds respectively however the method is not explained. I managed to calculate the answer to part d at one point but cannot remember how i got there :shy:

    Any help would be appreciated, thanks
     
  2. jcsd
  3. Jun 7, 2012 #2
    This really just boils down to saying, for example on part (b),

    [tex]\dot \theta = 3 \cos 3t = 2[/tex]

    Move the 3 over so you get [itex]\cos 3t = 2/3[/itex] and then use an inverse cosine function. That's really all there is to it; (d) is very similar.
     
  4. Jun 8, 2012 #3
    Ok thats great thanks!
     
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