This is what a typical motor startup behavior looks like, when a DC motor is powered by a constant voltage. These graphs are for a DC motor with plenty of winding groups, so that torque is independent of position. While this graph is for DC, the same principles apply for AC motors as well.
For the motor to start rotating from rest, it takes a high torque, which also means high current. This draws down the source voltage significantly, because of the voltage drop on the circuit that powers the rest of the building. The motor behaves very closely to a short circuit when initially starting. It takes time for the motor to get up to speed, where the windings can supply a sufficient back-EMF to reduce the current drawn, as it approaches its steady state operation. The more mechanical load and mechanical resistance to rotation you have, the more starting torque needed, and the greater the inrush current. Reducing mechanical friction can be a way to improve this issue.
Here's a typical diagram of the three behaviors of a motor. These all are part of the same physical component, the coils of wire.
And the system of equations that governs the motor:
Electrical: L*I'(t) = -R*I(t) - K*ω(t) + V
Mechanical: J*ω'(t) = K*I(t) - D*ω(t) - τ(t)
I(t) = current, I'(t) = rate of change of current, V = source voltage, t = time
ω(t) = rotor speed, ω'(t) = acceleration, J = rotor inertia, D = frictional drag coefficient (assuming proportional drag), τ = output torque
The solution to these equations, are damped oscillations that start at rest, and settle to the steady state running condition. Graphing speed vs current, will look like a spiral.
The Back EMF element, is the element we want to deliver power to, as it is the element that converts electric power to mechanical power. Its voltage drop, is proportional to its rotation speed, so at rest, it is a short circuit element. The inductance (L) and resistance (R) are the only two elements that impede the current at that time. Ideally, R is as small as possible, since this is heat loss in the windings. The energy delivered to L goes into forming the magnetic field of the windings, instead of its mechanical output. This is what's happening, the instant the motor is turned on. The current grows quickly as the motor starts up, until it reaches its maximum inrush current.
As the motor achieves its running speed, the back EMF takes on a larger share of the voltage drop, and more of its power is delivered to the mechanical output (as we desire). This is what turns around the growth in current, so it can settle down to its steady state full load current.
This is why motors made today, are equipped with soft-start drivers, to mitigate this issue. These devices provide a gentle ramp up to the full running speed, so they don't draw the full inrush current right away. Variable frequency drives (VFD's) can also mitigate the issue by controlling the running speed with the frequency of the voltage source to the motor, as its speed builds from rest.
