Mechanics
What Mechanics tests
The Mechanics domain tests kinematics, Newton’s laws, momentum and energy conservation, circular and rotational motion, gravitation, and simple harmonic motion. Questions often combine a force analysis with an energy or momentum shortcut, so identify the conserved quantity before doing algebra.
Core rules
- For constant acceleration: v = v0 + at, x = x0 + v0t + (1/2)at^2, and v^2 = v0^2 + 2a(x − x0).
- Newton’s second law is a vector equation: ΣF = ma. The normal force is a constraint force, not automatically mg.
- Momentum is conserved when net external impulse is zero; mechanical energy is conserved only when nonconservative work is zero.
- Uniform circular motion requires a net inward force Fc = mv^2/r, supplied by tension, gravity, friction, or a normal component.
- Torque τ = rF sinθ changes angular momentum; static equilibrium requires both net force and net torque to be zero.
Worked example
A 2.0 kg block starts from rest and slides 5.0 m down a frictionless 30° incline. Find its speed at the bottom and the normal force.
Energy conservation gives mgh = (1/2)mv^2. The vertical drop is h = (5.0 m) sin30° = 2.5 m. Then v = √(2gh) = √(2 × 9.8 × 2.5) = 7.0 m/s. The normal force balances the perpendicular component of weight: N = mg cos30° = (2.0)(9.8)(0.866) = 17 N. The acceleration along the incline is g sin30° = 4.9 m/s^2, consistent with v^2 = 2as.
Traps
Using N = mg on an incline; mixing g = 9.8 and g = 10; treating centripetal force as an extra force rather than a net force; forgetting that kinetic energy is scalar while momentum is vectorial; using the wrong lever arm for torque.