Final answer:
The starter motor, which includes a small pinion gear, is responsible for engaging the engine's flywheel, transmitting power, and initiating the engine's rotation in a cranking circuit.
Step-by-step explanation:
In a cranking circuit, the component that uses a small pinion gear to contact the engine flywheel gear teeth and transmits starter motor power to rotate the engine is known as the starter motor. This device is essential in initiating the engine's operation by spinning the engine to a speed sufficient for the ignition process to take place. Inside the starter motor, the electrically powered motor turns the pinion gear, which then engages with the flywheel's gear teeth to crank the engine.