Mechanics

Forces, motion, energy · 8 formulas

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Newton's Second Law

F=maF = ma

Force equals mass times acceleration: heavier objects need more push.

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Hooke's Law

F=−kxF = -kx

A spring pushes back proportionally to how far you stretch it.

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Newton's Law of Universal Gravitation

F=GMmr2F = \frac{GMm}{r^2}

Every mass attracts every other mass; force drops with the square of distance.

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Kinetic Energy

KE=12mv2KE = \frac{1}{2}mv^2

Energy of motion: doubles with mass, quadruples with speed.

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Centripetal Acceleration

ac=v2ra_c = \frac{v^2}{r}

Moving in a circle requires constant inward acceleration; faster or tighter = more.

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Projectile Range

R=v2sin⁡(2θ)gR = \frac{v^2 \sin(2\theta)}{g}

Launch angle of 45° maximizes range; steeper or flatter angles fall shorter.

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Work-Energy Theorem

Wnet=ΔKE=12mvf2−12mvi2W_{\text{net}} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2

Net work on an object equals the change in its kinetic energy.

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Simple Harmonic Motion Period

T=2πmkT = 2\pi\sqrt{\frac{m}{k}}

Heavier masses oscillate slower; stiffer springs oscillate faster.