Laws of Motion
What this domain tests
Laws of Motion tests Newton's three laws, inertia, momentum, impulse, friction, circular motion and equilibrium. Numerical questions often involve lifts, pulleys, inclines, banking and friction limits.
Core rules
- Newton's second law: F_net = ma = dp/dt. First law defines inertial frames; third law pairs act on different bodies.
- Impulse = FΔt = Δp. Momentum is conserved when net external force is zero.
- Static friction satisfies f_s ≤ μ_sN; kinetic friction f_k = μ_kN. Friction opposes relative motion, not necessarily applied force.
- For circular motion, centripetal acceleration a_c = v²/r = ω²r, directed to the centre. Centripetal force is the net inward force, not an extra force.
- On a banked road without friction, tanθ = v²/(rg). In a lift, apparent weight N = m(g ± a).
Worked example
A 5 kg mass hangs from a spring balance in a lift accelerating upward at 2 m/s². Take g = 10 m/s². The forces on the mass are tension T upward and weight mg downward. Newton's second law upward: T - mg = ma, so T = m(g + a) = 5(10 + 2) = 60 N. The balance reads 60 N, greater than the true weight 50 N. If acceleration were downward, T = m(g - a).
Traps
Do not pair action and reaction on the same body. Static friction is not always μN; it adjusts up to a maximum. In a conical pendulum or banked curve, do not add a separate centrifugal force in an inertial frame. Check whether acceleration is upward or downward before choosing g ± a.