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Math Help - Torque problem

  1. #1
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    Torque problem

    Er = la = l(w^2 - w0^2)/2*theta

    this is for Torque i believe

    A CD has a mass of 17 g and a radius of 6.0 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 18 rad/s in 0.70 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.
    in Nm

    i could convert 17 to kg if i needed to.

    i know the angular velocity starts at 0.

    and the final angular velocity is 18.

    if i use angular kinematics i can use theta f = theta i + 1/2(wi + wf) * t

    to get theta f = 6.3
    i believe.

    so i'm not sure why this does not work: radius = 6 ... 6 x 2 = 12 cm (diameter)

    so then, 12(18^2 + 0^2)/ 2*(6.3)

    I got 308.57 N*m and that is not correct.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by rcmango View Post
    A CD has a mass of 17 g and a radius of 6.0 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 18 rad/s in 0.70 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.
    I'm not sure where you got your method, nor your last equation.

    \sum \tau = I \alpha
    where
    I = \frac{1}{2}mr^2

    So as you said:
    \omega = \omega _0 + \alpha t

    18 = 0 + \alpha (0.70) \implies \alpha = 25.7143~rad/s^2

    So
    \sum \tau = \frac{1}{2}(0.017~kg)(0.06~m)^2(25.7143~rad/s^2) = 7.869 \times 10^{-4}~Nm~rad

    (I personally prefer the Nm rad unit for torque. Most others don't.)

    -Dan
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