From AP to Competition: Master the F=ma and Make USAPhO

Track your past-exam progress with a color-coded Google sheet that records correct, almost, or incorrect answers, links official solutions by year, and shows cutoff scores to gauge readiness for USAPhO.

Learn to solve physics problems with symbols, not numbers, to see dependencies, check dimensions, and test general cases before plugging in numbers.

Master dimensional analysis by distinguishing basic and derived dimensions, balancing dimensions, and deriving relationships such as period of a mass-spring using F=ma and Hooke's law, showing t proportional to sqrt(m/k).

explain limiting cases in f=ma problems, using zero normal force, static friction thresholds, and extreme values to analyze collisions, tension, and gravity with inequalities and value plugging.

Explore translational and rotational kinematic equations relating position, velocity, acceleration, and time under constant acceleration. Learn to use delta notation and initial and final values to solve for missing quantities.

Master two-dimensional projectile motion by using initial velocity and angle to determine range and maximum height, while separating vertical and horizontal motions with key kinematic equations.

Learn how rotating the coordinate system to align with a slope simplifies projectile motion by decomposing velocity and gravity into components, enabling easier calculation of distance to impact.

Master 1D and 2D relative motion by choosing a frame of reference, applying VB minus VA in the ground frame, and using vector and triangle methods.

Demonstrate the rigid body concept by enforcing zero relative velocity along a rod, so VA equals VB along the rod, with a sliding rod on a wall and floor example.

Explore Newton's laws, focusing on using free-body diagrams and F=ma to solve force and acceleration problems, with emphasis on the third law and momentum conservation.

Extend Newton's laws to rotational motion by mapping torque, torque diagrams, rotational inertia, lever arms, and angular acceleration to force, mass, and linear acceleration.

Explore contact forces such as tension and normal force and how they differ in static situations. See how they act along ropes and perpendicular to surfaces on inclined planes.

Learn the friction force and its static and kinetic forms, determine direction and magnitude from forces, and apply inequality for maximum static friction with normal force and coefficient of friction.

Explore rolling without slipping as a combination of translational and rotational motion, linked by static friction and v equals r omega, including the incline acceleration formula with beta.

Explain uniform and non-uniform circular motion by detailing centripetal acceleration towards the center and how net forces equal m v^2 / r, with examples like gravity, friction, and pendulums.

Compute torque using radius and force with cross products or the lever arm; understand torque direction via the right-hand rule and balance torques for static equilibrium.

Solve a static torque problem with three identical rigid rods to determine the fraction of total weight resting on the left leg by using torque balance and lever arms.

Examine the elastic spring force via Hooke's law, rest length, and displacement, and apply energy concepts—including 1/2 k delta x^2—to static and oscillating systems with gravity and equilibrium.

Model springs in series and parallel and determine their equivalent spring constant. Apply Hooke’s law to connect forces and displacements in each arrangement.

Explore Young's modulus, the stress–strain ratio E, and how to solve for missing variables in F=ma style problems by applying force, cross-sectional area, and the fractional change in length.

Explore how pulleys redirect forces with massless strings, keep tension equal along the string, and apply conservation of string length to analyze movable and fixed pulleys and their double movement.

Explains the four energy types: kinetic, gravitational potential, elastic potential, and heat energy; shows translational and rotational kinetic energy, rolling without slipping, and energy conservation in oscillations and inelastic collisions.

Explore how work equals the dot product of force and displacement. Use parallel components via F d cosine theta; perpendicular forces do no work, and signs relate to energy.

Explore how conservative and non-conservative forces govern work and energy, linking force, work, and potential energy, and clarify sign conventions in the F=ma context.

Explore the conservation of energy by equating initial and final total energy, including gravitational potential energy, kinetic energy, and heat energy, while recognizing when energy is dissipated or lost.

Explore the center of mass as the reference for gravity and torque, calculate it with the sum of m_i x_i over the total mass, and use the centroid for triangles.

Learn to define a system of objects, distinguish internal and external forces, and use center of mass and total momentum to analyze collisions and conservation laws.

external forces cause acceleration of a system as a whole, while internal forces cancel out; treat the system as one object, as shown by the sailboat and skateboard examples.

Explore conservation of momentum, distinguishing linear and angular momentum and their conditions. Learn how external forces and torques affect momentum, and use the center-of-mass velocity to simplify problems.

Explore how impulse changes momentum through force applied over time, noting mass may vary and that impulse equals the area under the force-time curve or its integral.

Explore two-body collisions, mass and velocity variables, and momentum conservation, then classify elastic, inelastic, and perfectly inelastic collisions, using the coefficient of restitution to distinguish them.

Solve inelastic collisions using conservation of momentum with less information than elastic cases. Determine final velocities and the change in kinetic energy, noting perfectly inelastic collisions where objects stick together.

Explore elastic collisions by applying momentum conservation and using a shortcut: the relative velocity reverses after impact; compare the center-of-mass frame method with the relative-velocity trick.

Learn gravity through Newton's universal law of gravitation and the inverse-square relationship. Explore gravitational force, gravitational field, potential energy, and work near Earth.

Define escape velocity as the minimum speed to leave a body's gravitational influence forever, derived by conservation of energy from initial kinetic and potential energies to infinity.

Explore how elliptical orbits follow Kepler's first law, contrast with circular orbits, and apply energy and angular momentum conservation, using apoapsis, periapsis, and vis-viva to compute velocity.

Apply Kepler's laws to orbital motion. Bodies travel in ellipses with a sun at a focus, sweep equal areas in equal times, and relate period to the semi-major axis.

Learn how to change between circular orbits with a Hohmann transfer, using an elliptical link and two thrusts to compute delta-v with energy and the Vis-Viva equation.

Explore simple harmonic motion, a restoring-force oscillation (mass on a spring or pendulum) with displacement proportional to force, by sinusoids and linked to amplitude, period, frequency, and ω = 2πf.

Derive the period of simple harmonic motion by using a = -ω^2 x from a restoring force, then compute ω and T = 2π/ω, with a vertical spring example.

Explore rotational oscillations by applying Newton's second law for rotation, deriving alpha equals negative omega squared theta, and using small-angle approximations to analyze a rod pendulum's restoring torque and period.

Explore how to calculate the period of simple harmonic oscillations for mass-spring, pendulum, and physical pendulum systems using key formulas and dimensional analysis to relate period, mass, length, and gravity.

Master error propagation by examining how measurement uncertainty spreads through calculations for the F=ma exam, applying rules for absolute and relative uncertainties in addition, subtraction, multiplication, division, and powers.