Why do refrigeration compressors stall when switched off and on quickly; or, why do I need to wait three minutes before restarting my air conditioner?

The compressor compresses coolant on one side of a closed loop. If you shut off the compressor, you still have the load side of the closed loop full of pressurized coolant. That pressurized coolant makes it much more difficult to start the motor. A motor starting at 0 RPMs will want to draw large amounts of current. With an added load to the motor (pressurized coolant) the motor will draw excessive current and won't turn over.

Compressors are likely leaky and therefore will allow the pressurized side to slowly decrease pressure until it's equal pressure between tho two sides. If you wait 3 minutes, it's expected that the pressures balance out and you have virtually no load when you try and start the motor again.

A compressor running at speed has one side of the closed loop pressurized and so is under load, but in that case, it already has momentum to keep it going. Also, at speed the motor doesn't need as much current to continue spinning.

Here's a graph depicting induction motor torque and current vs speed to help illustrate why this happens.

The answers regarding built-up pressure are correct, but there's another aspect which hasn't yet been mentioned. In order for an induction motor to produce torque, it must have within it a magnetic field which is rotating at a particular speed (called the synchronous speed). Assume a particular motor is set up to run at a synchronous speed of 600rpm from 60Hz current. The magnetic field will then have six north poles and six south poles in a circle. When the "hot" wire is positive, the coils will try to drive the magnetic field so that the north poles are at the 12, 2, 4, 6, 8, and 10 o'clock positions, while the south poles are at 1, 3, 5, 7, 9, and 11 o'clock. When the "hot" wire is negative, the coils will try to drive the field so the poles are the opposite. If the motor is turning clockwise at slightly under 600rpm and a particular pole was at the 3 o'clock position at some point of time, then 1/120 second later that pole will be almost to the 4 o'clock position and the motor coils will try to pull it the rest of the way. If the motor was spinning counter-clockwise, then a pole which was at 3 o'clock at some point would be almost to the 2 o'clock position when the coils try to pull it the rest of the way. Note that the coils don't care which way the motor is turning--they rely upon its momentum for that.

To start such a motor, it's necessary to arrange things so that rather than simply going between two active positions, it goes between three or four. Typically this may be done by adding a capacitor and additional coils, so that on one line phase the motor will initially be pulled toward 12:00, 2:00, etc. but then soon thereafter to 12:10, 2:10, etc. Then on the next phase it will be pulled toward 1:00, 3:00, etc. followed by 1:10, 3:10, etc. Since 12:10 is a little closer to 1:00 than 11:00, the phase which tries to pull toward even numbers will apply a little clockwise torque. This amount of torque will be much smaller, however, than what could be produced if the motor were already spinning at a significant speed.

DC brush motors driven with a given voltage will produce maximum torque when they are starting or stalled. Likewise with AC induction motors which are driven with multiple "strong" phases. Most compressor motors powered by house current, however, produce near-zero torque at near-zero speeds. When there is no back pressure, the motors don't need to produce much torque to start moving; once they're moving, back pressure will increase, but so will their ability to produce torque. Shortly after a compressor is stopped, however, it will be unable to produce significant torque (since it's not turning) but will be unable to move without producing significant torque (because of the pre-existing back pressure).

Note that it is possible to engineer induction motor assemblies driven by house current to have a high starting torque but the cost of the motor will be greatly affected by the amount of starting torque required. If an application won't generally require a high starting torque, there's no reason to spend extra money on a motor that can produce it.

Most fridge motors have an extra winding for starting only.

This is initially powered via a PTC resistor, which when cold allows a high current to flow in the starting winding.

The PTC soon warms up and with increased resistance reduces the start winding current to an insignificant value. Continued but reduced current maintains the PTC in a hot, high resistance state while the motor runs.

When attempting to restart a recently-run motor, the resistance is still too high. Only after cooling for a few minutes does the resistance and hence starting current return to the required value.

A very hot compressor (stalled) with the PTC in proximity may require rather more than the normal few minutes to cool down.