📘 How do you solve mechanics problems?

What you’ll learn

1. One-Dimensional KinematicsApply kinematic equations to solve constant-acceleration problems in one dimension with explicit unit tracking.Position, velocity, and acceleration are linked by three equations derived from calculus. Students substitute given values and isolate unknowns while preserving significant figures. A worked example shows how initial conditions determine the parabolic position-time graph.
2. Projectile MotionResolve velocity vectors and apply independent horizontal and vertical kinematic equations to find range and maximum height.Horizontal velocity remains constant while vertical motion follows free-fall equations. Trigonometric decomposition separates components. A numerical example calculates time of flight and landing position for a symmetric trajectory.
3. Newton's Second Law ApplicationsDraw free-body diagrams and resolve forces to apply F = ma in two dimensions.Vector addition of weight, normal, and friction forces yields the net force. Students practice coordinate rotation to simplify inclined-plane problems. The resulting acceleration matches measured values within experimental error.
4. Work-Energy TheoremCalculate work as the dot product of force and displacement and equate it to change in kinetic energy.Work equals the integral of F·dx and equals ΔK for net work. Students evaluate work by constant and variable forces using graphs. The example converts kinetic-energy loss directly into braking distance.
5. Conservation of Mechanical EnergyApply conservation of gravitational potential plus kinetic energy to spring-mass systems without dissipation.Total mechanical energy remains constant when only conservative forces act. Students set initial potential equal to final spring energy and solve the resulting quadratic. The solution matches the turning point found by dynamics.
6. Linear Momentum and CollisionsApply conservation of momentum in two dimensions to elastic and inelastic collisions.Momentum is a vector conserved in isolated systems. Component equations yield two independent relations. The worked collision determines both magnitude and direction of the unknown velocity.
7. Rotational KinematicsUse rotational kinematic equations analogous to linear motion with consistent angular units.Angular displacement, velocity, and acceleration obey the same three equations with θ, ω, and α. Students convert revolutions to radians before substitution. The example illustrates the link between linear speed and radius.
8. Torque and Rotational DynamicsCalculate torque as r × F and apply τ = Iα to rigid-body rotation about a fixed axis.Torque equals the moment of inertia times angular acceleration. Students identify the perpendicular lever arm and sign convention. The numerical case converts linear force into rotational acceleration.
9. Angular Momentum ConservationApply conservation of angular momentum when external torques are negligible.L = Iω remains constant for isolated systems. Students equate initial and final angular momentum and solve for final ω. The example demonstrates the increase in rotational speed with reduced radius.
10. Simple Harmonic MotionDerive period, frequency, and energy relations for mass-spring and pendulum oscillators.Restoring force proportional to displacement produces sinusoidal motion. Students relate angular frequency to sqrt(k/m) and calculate amplitude-dependent maximum velocity. Energy oscillates between kinetic and potential forms.
11. Gravitation and Orbital MotionApply Newton's law of gravitation and centripetal force balance to circular orbits.Gravitational force supplies the centripetal acceleration for circular motion. Students equate GMm/r² to mv²/r and solve for speed. Kepler's third law emerges directly from the same equations.
12. Integrated Problem-Solving StrategiesSynthesize multiple conservation laws and kinematic relations to solve multi-stage mechanics problems.Complex problems require sequential application of energy, momentum, and kinematics. Students identify conserved quantities at each stage and match boundary conditions. The final numerical result is verified by an independent dynamics check.

Questions this course answers

Grounded in trusted sources

• Massachusetts Institute of Technology OpenCourseWare
• National Institute of Standards and Technology
• American Physical Society
• David Halliday, Robert Resnick, and Jearl Walker, Fundamentals of Physics — kinematics through gravitation
• Hugh D. Young and Roger A. Freedman, University Physics — mechanics problem methods
• Daniel Kleppner and Robert Kolenkow, An Introduction to Mechanics — careful Newton / energy treatments
• MIT OCW, Classical Mechanics (Walter Lewin / 8.01) — worked problem intuition, https://ocw.mit.edu/
• OpenStax University Physics Volume 1 — free mechanics text, https://openstax.org/details/books/university-physics-volume-1

Every Wunder lesson is built from real, reputable sources — never invented.

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