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Homework Help: Calculate the number of revolutions the disc makes

  1. Dec 8, 2005 #1
    A disc of moment of inertia 29.1 kg m2 is made to rotate about an axis through its centre by a torque of T . The disc starts from rest and, after {t} s, has kinetic energy {k} J.

    The torque is removed when the disc is rotating at 8.0 rad s-1 . An opposing torque of 13.2 N m is applied to slow the disc down.

    Calculate the number of revolutions the disc makes after the second torque is applied, before it comes to rest.

    how do i approch this problem (if numbers were involved) i would have to calculate the angular acceleration and then tention. after t seconds
    any help would be apprecated thanks in advance
     
  2. jcsd
  3. Dec 8, 2005 #2

    Fermat

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    This is a problem in rotational kinematics.

    Could you do it if it were a problem in linear kinematics, in other words, suppose you have a mass of 29.1 kg, with an initial speed of 8 m/s and a resisting force of 32.2 N, could you work out the distance travelled until it stopped ?

    What (kinematic) eqns would you use to solve that problem ?

    The eqns needed for the rotational problem are identical in form with their linear counterparts.

    e.g.
    s = ut + (1/2)at² - linear
    θ = ωt + (1/2)αt² - rotational

    If you know the eqns to use for the linear problem, then just convert them to their rotational equivelents.
     
  4. Dec 8, 2005 #3
    hi, er... well... i've got the following data...

    s=?
    u=8
    v=0
    a=? (-8/t)
    t=?

    s= ut + 0.5at^2 ------> s= 4t

    is the initial force equal to the resisting force. so that the force at the end equals 0
     
  5. Dec 8, 2005 #4

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    The resisting force is the decelerating force and is constant throughout the travel, s, of the mass.
    Use newton's 2nd law, F = ma, to get a numerical value for the deceleration. call it a.

    You need to use another kinematic eqn as well, though.
     
  6. Dec 8, 2005 #5

    Fermat

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    It's time I got some sleep (it's 1.00 a.m. here) so it's time I was off. Here's how to do it.

    Use the eqn of motion,

    v² = u² - 2as

    where v is the final velocity (v = 0) and u is the initial velocity (u=8) and a is the deceleration (a = -2.2045 m/s²).

    You will get a distance moved of,

    s = 14.515 m
    ==========

    Now all you have to do is write out the solution using rotational eqns of motion.

    Substitute for,
    s = θ
    u = ω
    a = α
    The numerical values in your rotational eqns will be identical to those used in the linear eqns and the final angular displacement will be θ = 14.515 rads.
    If you have been having any problems handling rotational eqns of motion, then after you've done it this way a few times, you will be able to just use the rotational eqns of motion straight away.
     
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