# On torque and work having same units

1. Apr 22, 2008

### benabean

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.

2. Apr 22, 2008

### Shooting Star

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 http://en.wikipedia.org/wiki/Torque" [Broken].

Last edited by a moderator: May 3, 2017
3. Apr 24, 2008

### Redbelly98

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

4. Apr 25, 2008

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??

5. Apr 25, 2008

### 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).

6. Apr 26, 2008

### benabean

Thanks guys, you're help is very appreciated.