Fundamentals of Mechanics

Mechanics Revision Sheet

1. 📌 Essentials

• Newton's second law: $= ma$ — fundamental for dynamics.
• Equilibrium: $\sum F = 0$, $\sum \tau = 0$ — static conditions.
• Work-energy theorem: net work equals change in kinetic energy.
• Impulse: $J = F \Delta t = \Delta p$ — describes collisions.
• Moment of inertia ($I$): depends on mass distribution; key in rotational motion.
• Simple harmonic motion: $x(t) = A \cos (\omega t + \phi)$, $T = 2\pi \sqrt{\frac{m}{k}}$.
• Conservation of energy: total mechanical energy remains constant in ideal systems.
• Friction: $F_f = \mu N$; static vs kinetic.
• Power: $P = \frac{W}{t}$ — rate of work.
• Mechanical advantage: ratio of load to effort in levers and pulleys.

2. 🧩 Key Structures & Components

• Displacement / Velocity / Acceleration — describe motion in kinematics.
• Forces — gravity, friction, tension, normal force.
• Mass and Shape — influence moment of inertia ($I$).
• Springs — characterized by spring constant $k$, oscillate in SHM.
• Levers / Pulleys — mechanical systems to amplify force.
• Friction surfaces — static and kinetic coefficients ($\mu_s, \mu_k$).
• Rotational Axes — points about which objects rotate.
• Energy reservoirs — kinetic energy, potential energy (gravitational).

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