How to diagnose a bad air conditioner motor
There are three major motors used in an air conditioning system: the compressor motor, the outdoor fan motor, and the indoor blower motor. Residential systems run off a single phase electrical system either with one (125V) or two legs (250V). What I will explain here will apply to both situations.
Take a look at the figure below. 
In this figure we show a typical single phase motor. The wires run to the motor are the black, white and red. The black and white wires are the normal L1 and L2 from your power source. The red wire may not always be red. Sometimes this wire can be brown, yellow, blue or another color depending on the manufacturer. In this explanation I am going to stick with red for simplicity. The black and white wires connect forming a circuit and the motor winding in this circuit creates a resistance measured in Amperes. The black and red wires run a different winding and also create a resistance measured in amperes. Inside the motor, all three wires are connected and you can run a circuit by using any combination of two of the three wires.
Determining a motor with an electrical problem: A motor can fail either mechanically or electrically. We will discuss the electrical failing here. There are three ways for the motor to fail electrically. First is a short to ground. Second is a disconnected short, and third is a short to another lead.
A motor that has not failed has a measurable resistance that will always be true for operational motors. First is the resistance property. Connecting a resistance meter from the black to the white leads should give you a resistance reading. Changing the leads to the black and red will give you a second reading. Changing the meter to the white and red leads will give you a third reading. The readings will be interrelated in such a way that you will know a problem exists if the relationship is not correct. Take the first reading and lets call that one R1, the second reading R2, and the third reading R3. For single phase motors, the relationship is R1 + R2 = R3. This will always be the case.
For a short to ground situation, you can put a lead on one of the three terminals and the other on a bear metal point on the motor housing. If the meter registers anything but open line “OL” on a digital meter or zero (0) on an analog meter then you have a short to ground situation and the motor is bad. Check all three leads; none of them should have any continuity between the terminal and the housing.
For an open line short the circuit is broken between two of the three terminals. You can verify an open line short by connecting the meter to two of the terminals and identify an open line indication, a zero resistance or a no continuity indication. Check all three combinations; black to white, black to red, and red to white.
A short to short fault will be a two-step test. The first step is to insure that there is continuity between the three terminals. Check black to white, black to red, and red to white. All should have continuity. Then check resistance. If the resistance calculation breaks the sum rule R1 + R2 = R3, or any of the resistance checks is zero, then you have a winding short.
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