Mechanics: Kinematics, Dynamics, Forces, Momentum and Equilibrium
Kinematics
SUVAT equations apply only to constant acceleration. Resolve into perpendicular components; horizontal and vertical motions are independent. For projectiles, vertical acceleration is g downward and horizontal acceleration is zero if air resistance is ignored.
Dynamics and momentum
Newton's second law F = ma for constant mass; weight is mg. Friction satisfies F ≤ μN until sliding. Momentum p = mv is a vector and is conserved in collisions and explosions when no external resultant force acts. Impulse FΔt = Δp, so a longer collision time reduces the force for the same change in momentum.
Equilibrium
For a body in equilibrium, resultant force is zero and resultant moment about any point is zero. Moment = F × perpendicular distance from pivot. A couple is two equal, opposite, parallel forces; its moment is Fd where d is the perpendicular separation. Resolve and take moments about a point to eliminate an unknown force.
Worked example
A ball is projected horizontally at 15 m/s from a 20 m cliff. Vertically, 20 = ½ × 9.81 × t², giving t = 2.02 s. Horizontal range = 15 × 2.02 = 30.3 m. Vertical velocity at impact = 9.81 × 2.02 = 19.8 m/s, so speed = √(15² + 19.8²) = 24.8 m/s. The horizontal velocity stays 15 m/s throughout.
Traps
Mixing sign conventions; using g = 10 when the data imply 9.81; assuming momentum is conserved when friction or a fixed pivot provides an external force; forgetting that the normal reaction changes on a slope; using the slope distance instead of perpendicular distance in a moment.