Force and Translational Dynamics
Force and Translational Dynamics
Newton's three laws anchor this domain: an object accelerates only under a net external force, a = F_net/m, and forces come in equal-and-opposite pairs acting on different bodies. Skill with free-body diagrams is the highest-value investment: isolate the object, draw only forces on it (weight, normal, tension, friction, applied, spring), then resolve along convenient axes. Friction obeys f_s ≤ μ_s N for static contact and f_k = μ_k N while sliding. Circular motion requires a net inward force of magnitude mv²/r, supplied by whatever real force acts (tension, gravity, friction, normal).
Traps: writing N = mg on an incline, in an elevator, or whenever another vertical force exists; treating static friction as always equal to μ_s N (it takes only the value needed for equilibrium, up to that maximum); adding a separate "centripetal force" arrow that is not a real interaction; and assuming tension is the same on both sides of a pulley that has mass or friction.
Worked example: masses 3 kg and 2 kg hang from a massless frictionless pulley. Treating them as one system, a = (m1 − m2)g/(m1 + m2) = (1)(9.8)/5 = 1.96 m/s², and T = m1(g − a) = 3(7.84) ≈ 23.5 N.
Rule of thumb: choose the system boundary so that internal forces cancel, then apply F_net = ma to that whole system.