# On torque and work having same units

## Main Question or Discussion Point

In rotational motion ,

the units for torque, $\tau = r \times F$,

are N $\cdot$ m

and for work done by a torque,

$W = \int_{\theta1}^{\theta2} \tau \cdot d\theta$, 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)

b.

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Shooting Star
Homework Helper
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.

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Redbelly98
Staff Emeritus
Homework Helper
N-m or N*m would be even better.

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??

rbj
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).

Thanks guys, you're help is very appreciated.