Physics · Ch 4 — Laws of Motion

Summary

Newton’s First Law (Law of Inertia): A body at rest stays at rest, and a body in uniform motion stays in uniform motion, unless acted upon by a net external force. Inertia is the property of mass — greater mass means greater inertia.
Newton’s Second Law: The net force on a body equals the rate of change of its momentum: $\vec{F}_{\text{net}} = \frac{d\vec{p}}{dt}$ . For constant mass, this reduces to $\vec{F}_{\text{net}} = m\vec{a}$ . Force and acceleration are always in the same direction.
Newton’s Third Law: Every action has an equal and opposite reaction. Forces always occur in pairs — action and reaction act on different bodies, so they never cancel each other.
Momentum: $\vec{p} = m\vec{v}$ . In the absence of a net external force, total momentum of a system is conserved (law of conservation of momentum).
Impulse: $\vec{J} = \int \vec{F}\,dt = \Delta \vec{p}$ . For a constant force, $\vec{J} = \vec{F} \Delta t$ .
Equilibrium: A body is in translational equilibrium when $\sum \vec{F} = 0$ . This implies either the body is at rest or moving with constant velocity.
Friction: A force opposing relative motion (or its tendency). Static friction: $f_s \le \mu_s N$ ; kinetic friction: $f_k = \mu_k N$ (usually $\mu_k < \mu_s$ ). Rolling friction is much smaller than sliding friction.
Circular Motion: For a body moving in a circle of radius $R$ with speed $v$ , centripetal acceleration $a_c = \frac{v^2}{R}$ directed toward the centre. The required centripetal force is $F_c = \frac{mv^2}{R}$ . …

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