Laws of Motion

Laws of Motion - Quick Revision

Aristotle vs Galileo. Aristotle: a force is needed to keep a body moving (wrong). Galileo (double inclined plane): a body in motion continues with constant velocity if no friction acts -> the law of inertia.

Newton's Laws

1. First law (inertia): if the net external force is zero, acceleration is zero. A body stays at rest or in uniform motion unless an external force acts. Inertia = resistance to change.
2. Second law: F = dp/dt = ma. Net force = rate of change of momentum. Vector law; local (no memory of past motion). 1 N = 1 kg m/s^2.
3. Third law: every action has an equal and opposite reaction. The pair acts on different bodies, simultaneously, with no cause-effect order, and cannot be added to give zero on one body.

Momentum & Impulse

• Momentum p = mv (vector).
• Impulse J = FΔt = Δp - useful for large forces acting for short times.
• Conservation of momentum: total momentum of an isolated system is conserved (follows from 2nd + 3rd laws). Holds in elastic AND inelastic collisions. Example: gun recoil.

Equilibrium

Friction

• Static f_s ≤ μ_s N (self-adjusting, opposes impending motion).
• Kinetic f_k = μ_k N (during sliding; independent of area, nearly of speed; μ_k < μ_s).
• Angle of repose: μ_s = tan θ_max (independent of mass).
• Rolling friction << sliding friction (why wheels matter). Friction is essential for walking, braking, driving.

Circular Motion

• Centripetal force F_c = mv^2/R = mω^2 R, directed to the centre. NOT a new force - supplied by tension/gravity/friction.
• Level road: friction provides F_c; v_max = √(μ_s R g) (independent of mass).
• Banked road: v_o = √(Rg tanθ) needs no friction; with friction v_max = √[Rg(μ_s+tanθ)/(1-μ_s tanθ)] > level-road value.

Common traps

• v = 0 does NOT mean F = 0 (ball at top of throw: a = g).
• mg = R only in equilibrium (differs in an accelerated lift).
• Don't put f_s = μ_s N unless motion is impending.