Mechanics
Core concepts
Newton's three laws, vector resolution of forces, static and kinetic friction, and the distinction between mass and weight anchor this domain. Be fluent with kinematics equations for constant acceleration, projectile motion (independent horizontal and vertical components), uniform circular motion (centripetal acceleration directed toward the center), work-energy and impulse-momentum theorems, and conservation of momentum in one and two dimensions. For rotation, know torque, moment of inertia, angular momentum conservation, and rolling without slipping.
Common traps
- Confusing the centripetal force with a separate outward force; there is no centrifugal force in an inertial frame.
- Applying constant-acceleration kinematics when acceleration is not constant.
- Forgetting that static friction has a maximum value but adjusts below it.
- Treating normal force as always equal to weight on inclines or in elevators.
- Momentum is conserved in collisions; kinetic energy is conserved only in elastic ones.
Worked example
A 2 kg block slides down a 30-degree frictionless incline from rest through a vertical drop of 5 m. Find its speed at the bottom. Energy conservation: mgh = ½mv², so v = √(2gh) = √(2·9.8·5) ≈ 9.9 m/s. Note the mass cancels and the incline angle is irrelevant for a frictionless drop.
Rule of thumb
Draw a free-body diagram before writing any equation; resolve forces along and perpendicular to the motion direction.