Electric start cranks and makes whirring sound but mower won't turn over.

There is little info here. There is some troubleshooting available in the sticky in this section.

Whirring doesn't really describe whether the motor is turning or the flywheel is being engaged.

The usual 1st order techniques apply:
1. Air (temporarily remove air filter)
2. Fuel (Is plug wet)
3. Spark (Remove plug and hold to block looking for spark)

Then you go for some details:
A. Will it attempt to start using carb cleaner squirted in the plug hole? Yes: Fuel problem, No: Timing or other issue; Check flywheel key

Since you say the engine doesn't turn over I would suspect the nylon gear on the starter bendix. This is the weakest part in a starting system and actually designed to be so. The gear slides down a candy cane shaft (bendix) and then slams into the engine flywheel. The teeth of the gears wear and chip so the flywheel won't get damaged. Open the starter and inspect that gear, they are about $4.