I Electric motor with increased load

[annamal]

How come when the load is increased in an electric motor, the torque and current increase but the motor slows? Isn't how fast the motor is how much torque it has?

 

[.Scott]

A combination of mass and speed of rotation yields angular momentum - not torque.
In the situation you are describing, an increase in the load causes the motor (and attached parts) to slow, so the angular momentum is also reduced.
But the motor is generating more torque - partially offsetting the increase in the load.

Here's an example: You are pedaling a bicycle and approaching a hill. When you reach the hill, your bike will slow (increase in load). If you don't pump harder, you will slow and ride backwards down the hill. So you pedal harder. You are still not traveling a fast as you were before. But you are applying much more torque.

 

[jbriggs444]

How come when the load is increased in an electric motor, the torque and current increase but the motor slows? Isn't how fast the motor is how much torque it has?

The truth is almost exactly opposite. For a given power output, an engine with the fastest rotation rate will have the smallest torque. Output power is the product of rotation rate and the torque the engine is applying to the load:

Let $P$ denote output power, $\omega$ denote the rotation rate and $\tau$ denote torque. Then $$P = \omega \tau$$For fixed P, and variable $\omega$, $\tau$ is given by $$\tau = \frac{P}{\omega}$$
But you are not holding power output constant. Instead, you seem to be holding the input voltage constant while changing the torque which is resisting the rotation. That is, you seem to be starting with an electric motor which is free-wheeling at its maximum rpm, generating zero (net) output torque and then applying a resisting load and expressing puzzlement that the rotation rate decreases as you try to resist the rotation.

There is no single formula for how the rotation rate of an electric motor changes in response to an applied load. You can google for things like "induction motor torque curve", "series motor torque curve". or "synchronous motor torque curve" to see some possibilities.