# torque for a machine shaft

this is a formula for torque and I was wondering for what P in this case stands for . . . • So no explanation in the source prior to this formula then? Aug 29 at 20:12

$$M_t = \frac{P}{2\pi\cdot n}$$

where:

• $$M_t$$ is the torque transmitted through the shaft (unit in SI: Nm).
• P is the power transmitted through the shaft (unit in SI: W).
• $$n$$ are the rotations of the shaft in revolutions per minute (rps). (this is important for the units to be correct)

If you want to use $$n$$ with revolutions per minute (rpm), you should use the following formula

$$M_t = \frac{60\cdot P}{2\pi\cdot n [rpm]}$$

(by square brackets next to a quantity I am presenting the units you should use in the equation)

As mentioned elsewhere another common equation (which basically incorporates the conversion between rpm and angular velocity) is the following:

$$M_t =\frac{P}{\omega}$$

where:

• $$\omega$$ is the angular velocity (units in SI: rad/s)

The relation of angular velocity with the rotations per second and minute correspondigly are $$\omega = 2\pi \cdot n[rps]$$ and $$\omega = \frac{2\pi \cdot }{60}n[rpm]$$

• thank you so much unfortunately we don't have any vaue for P provided. do you maybe know what value we could take (I edited my question so you can see how the construction should look like) Aug 30 at 12:43
• From what I understand you have a linear stage that is driven by a small stepper motor (engine in the image). as a starting point, you can use the power of the motor as P. You can obtain it using the rated voltage V times the rated current I (i.e. P = VI). You need to provide additional information about the setup and the engine in particular, in order to obtain a more useful answer. Aug 30 at 12:54
• thank you. we managed to get a value for P and solved the first equation for Mt. with the second equation where we have Fu, we're not sure what Fu stands Aug 30 at 13:20
• F refers to the force that develops at a distance of $\frac{d}{2}$ (d is the diameter of a pulley or a gear), when the applied torque is $M_t$. However, my recommendation is if you are not familiar with these equations, you should understand them first, before you try to plug number into them. Otherwise you can cause harm to yourself, or to equipment. Aug 30 at 13:24

$$P$$ is power.

$$P = \tau \omega$$

$$\tau = Torque$$

$$\omega = Angular Velocity (rad/s)$$

https://byjus.com/physics/relation-between-torque-and-power/