Physics

A wheel mounted on a stationary axle starts at rest and is given the following angular acceleration: 9-12t where t is the time after the wheel begins to rotate. Find the number of revolutions that the wheel turns before it stops ( and begins to turn in the opposite direction).

asked by Happinessdelight
  1. dv/dt = 9 - 12 t and v(0)= 0

    v = 9 t - 6 t^2 + constant
    when t = 0, v = 0 so constant = 0
    v is radians/sec

    v = 9 t - 6 t^2
    at v = 0
    0 = t(9-6t)
    so v = 0 at t = 0 as we knew
    and
    v = 0 at t=9/6 = 3/2 = 1.5
    so how far did it go?
    x is radians
    x = (9/2) t^2 - (6/3)t^3 + 0
    x = (9/2)(9/4) - (6/3)(9/4)(3/2)
    = 81/8 - 54/12
    = (243 - 108)/24
    =135/24 radians
    check my arithmetic
    divide by 2 pi to get revolutions

    posted by Damon

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