Mechanics and Properties of Matter
Core concepts
Newton's three laws, kinematics in one and two dimensions, projectile motion, circular motion, work-energy and impulse-momentum, conservation of momentum, torque and static equilibrium, and fluids (density, pressure, buoyancy, continuity, Bernoulli). Properties of matter includes stress/strain, elastic moduli, and thermal expansion as it relates to solids.
Traps to watch
- Mass vs. weight: weight is mg and changes with g; mass does not.
- Net vs. individual forces: a body moving at constant velocity has zero net force, not zero forces.
- Sign conventions: choose a positive direction and keep it through the whole problem.
- Projectile independence: horizontal velocity is constant (no air resistance) while vertical motion accelerates at g; time of flight depends only on vertical quantities.
- Circular motion: the net force points toward the center; "centrifugal force" is not a real force in an inertial frame.
- Buoyancy: the buoyant force equals the weight of displaced fluid, not the weight of the object.
Rule of thumb
When a problem gives forces and asks for acceleration or motion, draw a free-body diagram first and resolve into perpendicular axes. When it gives heights or speeds, energy methods usually beat kinematics.
Worked example
A 2 kg block slides from rest down a frictionless 5 m ramp inclined at 30 degrees. Find the speed at the bottom. Height h = 5 sin30 = 2.5 m. Energy conservation: mgh = ½mv², so v = sqrt(2gh) = sqrt(2 × 9.8 × 2.5) ≈ 7.0 m/s. Mass cancels - a common distractor is to include it.