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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“The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
—Marquis De Custine (1790–1857)