Save yourself the cost of a new motor. Check the capacitor first. When you turn on your pump and the motor produces a humming sound, the motor may be frozen so that it won't turn or you may have a bad capacitor. Check the capacitor. It can be replaced for a fraction of the price of a new motor. Note: Some motors have two capacitors: a run capacitor and a start capacitor. If so, check both.
Depending on the make of the pool pump, the capacitor will be under a hump cover on top of the motor, or it will be under a cover on the electrical end of the motor, or both. Some pumps have both a run capacitor and a start capacitor. The run capacitor will generally be rated at 15-50 MFD and 370 VAC. The start capacitor will generatlly be rated at 50-400 MFD and 125 or 250 VAC. This picture shows the location of the capacitor under a hump cover.
Pool Pump Capacitors store an electrical charge that can shock you even when the power is off. Before removing the capacitor, discharge this energy by placing a screwdriver across the leads of the capacitor. CAUTION: Capacitors have been know to explode when shorted out. For your protection wear eye protection and place a cloth over the capacitor before shorting it out.
If the capacitor is located at the end of the pool pump, remove the single screw that secures a clip holding the capacitor. Note how the plastic strip is positioned between the clip and the capacitor. It will have to be replaced in this position to keep the capacitor from shorting out on the motor. If the pool pump capacitor is on top of the motor, it should be free after you have removed the cover and the capacitor's leads.
Check the rating on the pool pump capacitor for replacement specifications. They will vary by manufacturer. Look for their MFD (or uf) and VAC specifications. For example, this one is a start capacitor rated at 124-149 MFD and 125 VAC. Try to replace the bad capacitor with an identical capacitor. If the exact capacitor is not available, you can use one with slightly higher capacitance. Do not use one with a lower rating.
Use a multimeter to verify that the capacitor is bad. Using the lowest ohms setting, touch the meter leads to the pool pump capacitor's terminals. If meter remains at 0, you know that the capacitor is bad. Check the new capacitor to verify it is good. First short out the terminals on the new capacitor to reset it. Then touch the meter leads to the capacitor terminals. If the capacitor is good, the meter will jump up to the other end than slower back off to 0.