The mechanical governor was invented by James Watt to regulate and limit, through feedback, the maximum speed of a steam engine. The device consists of two spherical masses connected via lightweight metal arms that can simultaneously rotate about a shaft and pivot outward from a hinge at the top, allowing the masses to rise depending on the rotation rate. Two more rods connect the arms to a collar that can slide up and down the shaft, controlling a lever that can be connected to a switch or valve that regulates the flow of fuel to the engine. In this case the governor is designed to cut off power when the shaft rotates at 139 rpm (or higher).

If the lever activates a switch when the mass arm makes an angle of ? = 61o with respect to the shaft, what length, L, should the connecting rod have to make the governor work as planned? Assume the connecting rods are made of very light weight material.

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