Before we dive deep into the working of a clutch and understand how a clutch works, let us just take a quick glimpse at the transmission system of a car.
The transmission system of the car is responsible for transmitting the energy from the engine to the wheels. When an internal combustion engine generates mechanical power, the pistons rotate the shaft attached to it. This rotatory motion is transferred through a shaft towards the wheels of the car.
The power generated by the engine is dependent on the acceleration and then the speed of the car is dependent on the power and the gear in the transmission system. So to have a smooth flow of the ride, the gears need to fit the speed of the car. To change the gears or to temporarily slow down the vehicle and keep the engine running, you need to disengage the connection of the shaft from the engine to the wheels. This is where the clutch does the work for you. The major science behind the working of the clutch is the frictional force. And, there are other natural laws behind its working.
Check this diagram of clutch for further understanding