Derive the formula for centrifugal force in a Watt governor, relating height, radius, arm length, and angular velocity.

Here are the solutions to your questions:

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Question 5.1
To determine the centrifugal force, we first need to find the angular velocity ($\omega$). For a Watt governor, the height $h$ of the cone formed by the arms is related to the radius of rotation $r$ and arm length $L$ by the Pythagorean theorem, and to the angular velocity by the governor's equilibrium condition.

Step 1: Calculate the height $h$ of the governor.
The radius of rotation $r$, the arm length $L$, and the height $h$ form a right-angled triangle, so $h = \sqrt{L^2 - r^2}$.

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