# Why the angular velocity in DC MOTORS = 0 when torque is maximum?

Why the angular velocity in DC MOTORS = 0. when the torque is maximum. is it supposed to be maximum with angular velocity and torque in the same time!

• " is it supposed to be maximum with angular velocity and torque in the same time!" - why would that be? Please consider adding your reasoning to your question. As it is, your question might attract down and / or close votes. – Alfred Centauri Mar 9 at 0:28
• Why Wouldn't?! the velocity must increase while the torque is increasing too. this is the reasoning! – Omar Einstein Mar 9 at 0:38

In general, if something is already moving, your ability to move it faster decreases. When you spin a merry-go-round, it's pretty easy at first. Once it's going at a very high speed, you can't supply any more force to it because it's moving almost as fast as your hands and arms can go.

Likewise an electric motor can't supply a lot of torque once it's up to high speed.

You should read the relationship with torque dependent on speed. A low speed means high torque is available, and high speed means only low torque is available.

The maximum torque that a DC motor can produce occurs at the 0 RPM or stall condition, because when the motor is prevented from turning there is no back EMF being generated to buck the flow of current through the rotor coils and there are no torque losses in the bearings or the cooling fan.

Similarly, the maximum RPM that a DC motor can produce occurs at the no load condition, where the motor is not applying torque to any load, and at which the back EMF equals the supply voltage.

Since power is the product of torque x RPM, the DC motor generates no power at the stall nor at the no-load speed, and its efficiency is zero at both conditions.

This means that somewhere inbetween these limits, the power output of the motor will go through a maximum, depending on the details of its manufacture.

The torque is a maximum when the current supplied to the motor is a maximum.

When a current flows through the coil of a motor, the coil rotates in a magnetic field and so the coil acts as a generator with the induced electromotive force (Faraday’s Law) in the opposite direction to the supply voltage $$\mathcal{E}_{\text{supply}}$$ (Lenz’s Law).

This is called the back emf, $$\mathcal{E}_{\text{back}}$$, and it is proportional to the speed of rotation of the coil.

For the circuit which contains the motor $$\mathcal{E}_{\text{supply}} -\mathcal{E}_{\text{back}} = I R_{\text{coil}}$$

Given that the back emf is proportional to the speed of rotation of the motor, as the rotational speed of the motor decreases the back emf decreases and so the current drawn by the motor increases.

The maximum value of the current occurs when the back emf is zero ie the coil is not rotating.

In practice when large dc motors are started because it takes time to get them up to speed the initial current would be so large that it would burn out the coil.
One way of preventing this is to introduce extra resistance in series with the motor to reduce the size of the current and hence the heating effect on the coil and then as the speed of the motor increased the amount of extra resistance in the circuit is reduced.