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On torque and work having same units

  1. Apr 22, 2008 #1
    In rotational motion ,

    the units for torque, [itex] \tau = r \times F [/itex],

    are N [itex]\cdot[/itex] m

    and for work done by a torque,

    [itex]W = \int_{\theta1}^{\theta2} \tau \cdot d\theta [/itex], are Joules.

    Yet both these quantities are homongenous/ have same SI units.

    Is it so wrong to quote torques in Joules? If so, why?
    (And vice versa)

  2. jcsd
  3. Apr 22, 2008 #2

    Shooting Star

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    Torque and work are two different types of quantities. Work done done is a scalar quantity, whereas torque is a (pseudo)vector.

    As a matter of interest, you are not even supposed to say mN for torque, but Nm.

    For more, read this.
  4. Apr 24, 2008 #3


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    N-m or N*m would be even better.
  5. Apr 25, 2008 #4
    they have the same dimensions, but so do the frequency of a sound wave and the rate constant of a first order chemical reaction. Does that mean you can express a rate constant in Hz??
  6. Apr 25, 2008 #5


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    you can use the same units if you want, but it might confuse some folks if you used Joules to describe a measure of torque.

    turning a shaft against X Nt-m of torque exactly one radian of twist requires X Joules of energy. measuring angles in radians is dimensionless (being the ratio of like-dimensioned quantities: arc length divided by radius).
  7. Apr 26, 2008 #6
    Thanks guys, you're help is very appreciated.
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