Mathematical Derivations
Most physics textbooks provide a simplified method of calculation that uses the mass of the bullet and pendulum and the height of the pendulum's travel to calculate the amount of energy in the pendulum, and thus the amount of momentum in the system. This ignores the small amount of momentum involved in rotating the pendulum. Robins' calculations were significantly more involved, and used a measure of the period of oscillation to determine the rotational inertia of the system.
Read more about this topic: Ballistic Pendulum
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“All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.”
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