The condenser fan motor.

The condenser fan motor drives the fan on the top deck of the outdoor unit. It pulls air through the coil fins and throws it straight up. That airflow is the only thing moving your house’s heat into the sky.

When it stops

A compressor running with no fan is a short story. Pressure and temperature climb fast, and the unit trips on its high pressure switch, usually within a few minutes. If a safety does not catch it, the compressor is at risk.

The symptom from inside the house is a system that cools for a few minutes, quits, waits, and tries again. From outside it is a unit that hums with a still fan on top.

It is often not the motor

A fan that will not start, hums, or needs a nudge to get going is far more often a dead capacitor than a dead motor. The capacitor is a fraction of the price. That is exactly the situation a second opinion exists for: being quoted a motor when the part that failed costs a tenth as much.

The honest test is a meter on the capacitor and an amp reading on the motor, which takes a few minutes and settles it.

What a replacement includes here

A universal replacement motor, with the matching run capacitor included rather than added on afterwards, at one published price. Where the unit sits does not change it.

Do not put a stick in a running fan to test it. It is a spinning blade in a live electrical cabinet, and the information it gives you is worth less than a hand.