how does torque get cars moving?

Answer 1

Torque is defined as twisting motion

The engine converts reciprocating motion into rotary motion.

The torque is produced by the stroke of the piston in combination with the force by combustion pushing on the piston. The longer the stroke the higher the torque.

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Answer 2

1 foot pound of torque is equal to the amount of 552 pounds being placed on a 1 foot long leaver.
It is the rotating power of a engine.
If a engine is rated at 300 ft pounds of torque at 4000RPM's, when the engine is turning 4000 RPM's it is putting out the same as 165,600 pounds on a one foot long leaver. This power is going to the drive train to move the vehicle.
Horse power is a separate measurement.