Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, mass m, maximum angle 0, and the strength of gravity g (with units [g]=m/s2), explain why we must have a relation like T = f(0) × √√.2 (Note that counts as a unitless parameter here.) Asserting ƒ(0) ~ f(0) in this formula is the small X 9 angle approximation (where f(0) = 2π is found by other means).

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Density of Solids

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.