Force and Translational Dynamics
Core ideas
Newton's laws anchor this domain. The first law defines inertia; the second, ΣF = ma, is a vector equation applied per axis; the third says forces come in equal-and-opposite pairs acting on different bodies. Candidates must construct free-body diagrams and resolve forces into components.
Key force models: weight (mg), normal force (perpendicular to surface), tension (along string), kinetic and static friction (f ≤ μN), and spring force (F = -kx). For systems of connected objects, treat them as a unit to find acceleration, then isolate one object to find internal forces.
For circular motion, the net inward force equals mv²/r; centripetal force is not a new force but the label for whatever real force points toward the center.
Traps
- Listing the "reaction" to a book's weight as the normal force - they are not a third-law pair (both act on the book).
- Assuming N = mg on inclines or when other vertical forces exist.
- Applying static friction as always equaling μN; it only reaches that maximum at slipping.
- Forgetting that a massless string has the same tension throughout an ideal pulley.
Rule of thumb
Draw the free-body diagram first, choose axes along the acceleration (tilt axes for inclines), then write ΣF = ma separately for each axis. Never put a "centripetal force" arrow on a diagram; identify the real force causing it.
Worked example
A 2 kg block on a frictionless 30° incline: the along-ramp component of weight is mg sin30° = 2(10)(0.5) = 10 N, so a = 10/2 = 5 m/s² down the ramp. The normal force is mg cos30° ≈ 17 N.