The physical principles behind car gears.
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This video offers an unusual perspective to the relation between engine power, RPM and acceleration.
1) Torque - a gear of radius R that exerts force F is said to have a torque of T=R*F. Engines do not produce force per se, but torque. So if the engine produces a torque of T, and that is transmitted unchanged to a gear of radius R, you a get a force of T/R.
The video offers an alternative view, where the relation between RPM, power and accelartion is explained without torques.
See more about torques in this video: http://www.youtube.com/watch?v=Sm4pV3xyJRE
2) Efficiency - this video assumes and ideal world with 100% efficiency. No energy is wasted on friction or any other mechanical losses.
3) Another simplifying assumption is that the engine produces a constant torque, and thus a constant force. As mentioned in one of the comments in the end, this is not the case with real engines. In most engines the torque rises as RPM rises, peaks at some RPM, and then starts to fall. Because of that the power does not steadily increase with RPM. It increases in the beginning, and continues to increase a little bit after the torque peaks. Then as the torque starts to dimish significantly, the power reduces as well.
4) Measurments - here are the measurments used in the simulation:
16 teeth gear radius: 18cm = 0.6 ft
Force exerted by this gear: 196N = 44.1 lb
Car wheel radius: 21cm=0.7 ft
Car weight: 352kg = 775 lb
5) The car wheels are slightly bigger than the 16-teeth gear, and this is adds up to the gear ratio effect. In the first car, for example, while the transmission box has a gear ratio of 1:1, the larger wheels cause an overall gear ratio of 1.18:1. This can be seen at time 2:25, where the wheel's power visualization is slightly elongated (a bit more speed and a bit less force).