On torque and work having same units

In summary, torque and work are two different types of quantities with different units: N-m and Joules, respectively. However, they both have the same SI units. It is not technically wrong to use Joules to describe torque, but it may be confusing to some people. The same principle applies to other quantities with the same dimensions, such as the frequency of a sound wave and the rate constant of a chemical reaction. It is important to use the appropriate units to avoid confusion.
  • #1
benabean
31
0
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)

b.
 
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  • #2
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].
 
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  • #3
N-m or N*m would be even better.
 
  • #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??
 
  • #5
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
Thanks guys, you're help is very appreciated.
 

1. What is torque and work?

Torque is a measure of the force that causes an object to rotate around an axis. It is the product of the force applied to an object and the distance from the axis of rotation. Work, on the other hand, is a measure of the energy transfer that occurs when a force is applied to an object and moves it a certain distance.

2. Why do torque and work have the same units?

Torque and work have the same units because they both involve force and distance. In torque, the force is applied at a distance from the axis of rotation, while in work, the force is applied over a certain distance. Therefore, both quantities have the unit of force multiplied by distance, which is represented as joules (J) in the SI system.

3. What is the relationship between torque and work?

The relationship between torque and work is that torque is a component of work. When a force is applied to an object, both torque and work are involved. Torque is responsible for causing the object to rotate, while work is responsible for moving the object in a linear direction. In other words, torque is a rotational force, while work is a translational force.

4. Can torque and work be calculated using the same formula?

No, torque and work have different formulas for calculation. Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation, while work is calculated by multiplying the force applied to an object by the distance it moves in the direction of the force. However, both formulas result in the same unit of joules (J).

5. Why is it important to understand the relationship between torque and work?

Understanding the relationship between torque and work is important because it helps in understanding the principles of rotational and translational motion. It also helps in solving problems related to mechanics and engineering. Additionally, knowing the relationship between these two quantities can also lead to a deeper understanding of other related concepts such as power and energy.

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