# Which is the part that's work applied at and rotates with a distance? [closed]

For the figure below I have a question that is: I see that the pink rod is the shaft and a gray circular body. What I can't get is that which one is the work being applied at and for which one does ($$n$$ = number of revolutions) relate to?

• The work is applied to whatever is connected to the shaft. Oct 17, 2021 at 16:04
• Bob D : do they both have the same speed? And why? Oct 17, 2021 at 17:41
• The both have the same rpm, or in the figure, the same $\dot n$. Oct 17, 2021 at 17:52
• Hello! It is preferable to type out screenshots or images of text; for formulae, one can use MathJax. Thanks! Oct 18, 2021 at 14:03

I think this text is about the wheel of a car and it's shaft (as a simplest example).

What I can't get is that which one is the work being applied at and for which one does(n=no.of revolution) relate to?

In physics, Work is not applied work is done the force is applied which causes the work to be done.
Here the force $$F$$ is applied in the tangential direction of the wheel and this produces the torque $$T$$.$$T = F \cdot r$$ The above statement is the definition of torque.(As a simple example to open a gate which is fixed to the wall with hinges you need to apply torque to it if you apply the force very near to hinges (pivot) you will need more force as the radius is small on the other hand if you apply the force farther from the pivot then you will need less force as the radius is bigger).
Now let's come to the distance problem:
It is very easy to calculate that how much distance is covers by a wheel in $$n$$ revolutions. It is $$n$$ times the circumference of the wheel as it is given in the text above.
Now for the work done:
Work done is defined as product of force and distance covered. $$W_{sh} = F \cdot s$$ therefore, $$W_{sh} = 2\pi nT$$ And since the shaft and the disc are connected thus it does not relate to anyone as both will have same number of revolutions .

What I can't get is that which one is the work being applied at and for which one does(n=no.of revolution) relate to?

Based on the figure showing the torque being applied by the gray disc, the work appears to be applied to whatever is connected to the shaft.

do they both have the same speed? And why?

Since the shaft and the disc are connected together, the must have the same rpm. In other words, $$\dot n$$ is the same for the disc and the shaft.

Hope this helps.