# A peculiar definition of work on Wikipedia

• etotheipi
In summary, the conversation discusses the calculation of work done by an external agent exerting force and torque on an object along a curved path. One participant questions the validity of a given definition and suggests alternative expressions. Another participant raises a concern about the application point of the force and the center of mass. Overall, it is concluded that the given definition may be incorrect and should be disregarded.
etotheipi
I came across this here:
The work done W by an external agent which exerts a force ##\vec{F}## (at ##\vec{r}##) and torque ##\vec{\tau}## on an object along a curved path C is: $$W = \int_{C} (\vec{F}\cdot d\vec{r} + \vec{\tau} \cdot \vec{n} d\theta)$$
Is this incorrect? If we setup any coordinate system and take torques about that coordinate system, then I would have thought we say the work done in that frame is $$W = \int_{C} \vec{F} \cdot d\vec{r} = \int_{C} \vec{\tau} \cdot d\vec{\theta} \quad \left( = \int_{C} \vec{\tau} \cdot \vec{n} d\theta \right)$$ So long as the curve ##C## represents the path of the point of application of the force. The definition Wikipedia gives appears to be double counting the work since we can show that the two expressions I equated are equivalent. I would however agree that another correct expression be $$W = \int \vec{F} \cdot d\vec{r}_{CM} + \int \vec{F} \cdot d\vec{r}' = \int \vec{F} \cdot d\vec{r}_{CM} + \int \vec{\tau}_{CM} \cdot d\vec{\theta}_{CM}$$ if ##\vec{r}'## represents the position of the point of application of the force w.r.t. the centre of mass.

I wondered whether anyone could clarify, since I'm not sure if the relation they gave makes any sense. Surely work is just ##\int \vec{F} \cdot d\vec{r}##? Thank you!

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etotheipi said:
I came across this here:

Is this incorrect? If we setup any coordinate system and take torques about that coordinate system,
Are you sure they take the torque around the origin, and not around the point defined by r?

etotheipi
A.T. said:
Are you sure they take the torque around the origin, and not around the point defined by r?

It doesn't specify, but even if it were about the the point ##\vec{r}## wouldn't it still be incorrect?

The only decomposition of that form which is meaningful is when ##\vec{r}## is to the centre of mass. But from the preceding statement it doesn't specify that the curve C is the path of the centre of mass. That is to say the the force need not be applied at the centre of mass of the body.

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I think it's a blunder; I'll ignore this definition!

## 1. What is the definition of work on Wikipedia?

The definition of work on Wikipedia is a bit different from the traditional definition. It is defined as "the process of exerting effort to achieve a goal or result." This definition focuses on the effort put in rather than the actual result achieved.

## 2. Why is the definition of work on Wikipedia considered peculiar?

The definition of work on Wikipedia is considered peculiar because it deviates from the commonly accepted definition of work, which is typically defined as "an activity involving mental or physical effort done in order to achieve a purpose or result."

## 3. Who came up with this peculiar definition of work on Wikipedia?

The peculiar definition of work on Wikipedia was proposed by user "B9 hummingbird hovering" in 2013. It has since been debated and discussed by other Wikipedia editors, but the definition remains on the site.

## 4. How does this definition of work differ from other definitions?

This definition of work differs from other definitions in that it places more emphasis on the effort put in rather than the end result. It also does not specify whether the effort is mental or physical, leaving it open to interpretation.

## 5. What is the purpose of having a peculiar definition of work on Wikipedia?

The purpose of having a peculiar definition of work on Wikipedia is to encourage critical thinking and discussion about the concept of work. It challenges the traditional understanding of work and invites readers to consider alternative perspectives.

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