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Moment of Inertia Help Pls.

  1. Jan 12, 2006 #1
    A spherical object has a(n) 54.4 m diameter.
    Its moment of inertia about a diameter is
    I = fMR^2, where M is its mass, R is its
    radius, and f = 0.302.
    The acceleration of gravity is 9.8 m/s^2
    Starting from rest, how long will it take this
    object to roll, without slipping, 10.88 m down
    an incline that makes an angle of 35.1 degrees with
    the horizontal? Answer in units of s.

    How does I figure this out without a given mass? Does it cancel out in the calculation?

    An approach to this and concepts involved in solving this would help greatly.

    I don't know, I don't like moment of interia nor torque. :(

    I have my final exam tomorrow, help is greatly needed and much appreciated.
  2. jcsd
  3. Jan 12, 2006 #2

    Doc Al

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    Staff: Mentor

    Start by identifying the forces that act on the object. Then apply Newton's 2nd law for both translation and rotation to find the acceleration of the object down the incline. (Since it rolls without slipping, figure out how the translational motion is related to the rotational motion.)
  4. Jan 12, 2006 #3
    Mgh= 1/2mv^2 + 1/2 Iw^2

    I can use v=Rw to substitute into the equation and eventually solve for v.

    But then how do I find alpha to solve for t?

    w= alpha * t
  5. Jan 12, 2006 #4
    Newtons second law... F=ma; torque=I(alpha)
  6. Jan 12, 2006 #5
    alpha = (gsin(theta))/(R + (I/mr))

    t came out to be equal to 2.24226 s. (which is correct :smile: )

    Thanks to all those that helped!:approve:
  7. Jan 12, 2006 #6
    Just a correction:

    dw = alpha * dt

    Good luck on your exam.
  8. Jan 12, 2006 #7
    Thanks... I really need an A. :)
  9. Jan 13, 2006 #8

    Doc Al

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    Staff: Mentor

    There's nothing wrong with solving the problem this way. Once you solve for the final velocity at the bottom of the incline, you can use simple kinematics to find the time. Hint: What's the average speed of the object as it rolls down the incline?
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