I know the formula that P=Tw, but I’m wonder that what if the power changes?

Keep in mind the formula:

\begin{array}{l}P=\tau .\omega\end{array}

Where, p is the power (work done per unit time), T, is the torque (rotational ability of a body), w is the angular velocity(rate of change of angular displacement), . represent the dot product or scalar product.

To get the torque needed to produce a particular angular velocity and power, the equation above can be modified. Power is introduced by the torque, which solely depends on the immediate speed.

**## Relationship Between Torque and Power**

Compare the linear equivalent for any rotatory motion to determine the relationship between torque and power. The product of the angle covered and radius determines the linear displacement, which is the distance traveled around the perimeter of the revolution. The intersection of radius and angular velocity yields the linear velocity. Additionally, the result of linear velocity and time is linear distance.

∴ Radius times angular velocity times time equals linear distance.

An item undergoes rotational motion due to torque. It is written as:

Torque = Force × Radius

\begin{array}{l}Force=\frac{Torque}{Radius}\end{array}

\begin{array}{l}Power=\frac{Force\times Linear;distance}{Time}\end{array}

\begin{array}{l}Power=\frac{\left ( \frac{Torque}{Radius} \right )\times Radius \times Angular ;velocity \times Time}{Time}\end{array}

\begin{array}{l}Power=Torque\times Angular;velocity\end{array}

I hope you comprehended the relationship and conversion between a rotating object’s power and torque.

Now truly, how does power of the motor change?

Note*

*> Due to the fact that a motor’s rated output power is a set amount, the connection between torque and speed is inversely proportional. The available output torque reduces correspondingly as output speed rises. The output speed reduces correspondingly as the output torque rises.*

For example, I know when the motor’s power is P, the torque is T and the speed is w

but what will happend if the power become P/2?or 2P?If the ratio did’t change.

If power doubles, then torque doubled, speed doubled, or some mathematical combination of the two took place so that their product is twice what it originally was. (technically torque could halve, speed could quadruple, and power would double)

Every gets hung up on power, or horsepower in automotive (internal combustion). Really it’s easier to measure/talk in torque because all those power ratings are peak power… and it’s seldom that you can stay right on top of the power curve to harvest peak output all the time, nor would you want to if you think about it.

For example, I know when the power is P, torque is T and speed is w.

And I’d like to know when the power is P/2, what will happend with torque and speed.I didn’t change any condition without the power.

First answer (the obvious one)… if power is half, of some prior value, then: torque is half, or speed is half, or some mathematical combination of the two is half.

Second answer (and what I think you are asking, or trying to ask)… if power is half do you have the ability for torque to be more, to have torque ‘in reserve’. The answer there is yes, with limitations. Torque will never exceed the ability of the engine/motor to provide it… torque curve shows max value available at different rpms.

I think what I’m trying to ask for is a way to compute the torque of the motor by the prior values.

Why not take the power & rpm readings from the motor and do the actual math? Your torque will end up as oz-in (ounce inches) if you handle your units properly.