AP Physics 1: The 14.5-Hour Fast Track to a Perfect Score

Explore kinematics, the study of motion, analyzing distance traveled, displacement, speed, velocity, and acceleration; compare average and instantaneous measures and visualize their graphs using calculus.

Define position relative to an origin, explain distance traveled as total path length, and displacement as the change from initial to final position, independent of path.

Velocity is a vector with positive or negative direction, while speed is its magnitude and always positive. Average velocity is displacement over time; average speed is distance traveled over time.

Explore how to find average and instantaneous velocity from position-time graphs by calculating slopes, translating between position and velocity graphs, and identifying turning points where velocity changes sign.

Explain acceleration as the change in velocity over time, including average and instantaneous forms, and the slope of the velocity-time graph. Use car examples and relate to velocity, position, inflection.

Relate position, velocity, and acceleration via the derivative; velocity is the limit of delta x over delta t and acceleration the derivative of velocity, shown with a polynomial position function.

Derive the four kinematic equations for motion under constant acceleration, linking acceleration to velocity change and displacement via velocity-time graph areas and equations x= ut+1/2 at^2 and v^2 equals u^2+2as.

Apply motion under constant acceleration using the four kinematic equations. Solve stopping, displacement, and catch-up time from given initial velocity, final velocity, acceleration, delta x, and time.

Explore free fall under gravity with a constant downward acceleration of 9.8 m/s^2. Observe velocity decrease to zero at the top and the ensuing motion, including ball bounces.

solve a kinematic free-fall problem from 100 meters using y_final = y_i + v_i t + 1/2 a t^2. analyze upward versus downward throws to find time and final velocity.

Learn how vectors in two dimensions have magnitude and direction, express components with unit vectors i-hat and j-hat, and convert between Cartesian and polar representations.

Convert vectors between polar and cartesian representations by computing x and y components from magnitude and angle using cosine and sine, then find magnitude and direction with Pythagoras and arctan.

Learn to add and subtract vectors by components, combining x, y (and z) components, use the head-to-tail method, and apply negative vectors with the same magnitude but opposite direction.

Explore adding vectors and calculating the change in velocity using polar form and components, with x and y decomposition, magnitude and direction via Pythagoras and arctangent.

Explore relative motion through reference and inertial frames, defining relative velocity as v_A/B equals v_A minus v_B and applying it to swimmers and currents to find total velocity.

Explore relative velocity with two examples, calculating total velocity, magnitude, and direction using vector addition, components, the Pythagorean theorem, and trigonometry.

Explore two-dimensional motion by treating x and y components separately, noting zero x-acceleration and gravity-driven y-acceleration of -9.8 m/s², with projectile and free-fall examples.

Explore two-dimensional motion through real examples, deriving x and y components using kinematic equations, analyzing initial conditions, accelerations, and delta time to compute positions and velocities.

Explore Newton's first law by defining force and acceleration, analyzing gravity and air resistance on a baseball and a ball released from a boat to illustrate motion at constant velocity.

This lecture applies Newton's second law by summing forces to obtain acceleration, using vector components, then uses kinematics to find the car’s final position after three seconds.

Explore gravity, normal force, and tension, and distinguish kinetic friction and static friction with their coefficients relative to the normal force.

Explore how the normal force balances gravity in vertical contact, and how, with an additional downward push, it equals gravity plus the push, via Newton's second law and two-dimensional analysis.

Explore Newton's second law with kinetic and static friction, computing acceleration and displacement using normal force, gravity, and coordinate components through book on a table, elevator, and fridge examples.

Solves an incline plane problem by resolving gravity, normal force, and kinetic friction into x and y components, applying Newton's second law to find the pulling force for 1 m/s^2.

Explore the range of forces to keep a book pressed against a wall at a 15-degree angle in equilibrium, balancing normal force, gravity, and static friction with Newton's second law.

Apply Newton's second law to two rope tensions on an acrobat, resolve forces into x and y components, and compute the resulting acceleration and the tension needed for zero acceleration.

Explore Newton's third law by examining how every interaction produces equal and opposite forces on two objects. See examples from gravity, normal forces, tension in pulleys, and friction.

Analyze a two-block system pushed by 30 N, applying Newton's second law to determine the contact force and the shared acceleration with friction neglected.

Explore Atwood's machine with a pulley and two masses, derive acceleration using Newton's laws, tension, and gravity; also analyze a frictional system with kinetic friction coefficient 0.2.

Analyze Atwood's machine variations with three rope and pulley setups to determine tensions and accelerations via Newton's second law. Relate rope lengths and pulley constraints to solve each motion.

Analyze gravitational forces, tensions, and accelerations in coupled block systems, and apply static and kinetic friction to determine maximum push while solving Newton's laws.

Explore uniform circular motion and centripetal acceleration, with magnitude v^2/r toward the center, and see how gravity, tension, and normal forces sustain such motion in the moon and teacups.

Apply Newton's second law to a rock on a string in uniform circular motion, analyzing tension and gravity's radial components to yield centripetal acceleration, period, and angle theta scenarios.

Analyze a uniform circular motion problem with friction, derive the normal force and centripetal acceleration, and determine the minimum and maximum speeds under static friction.

Explore how static friction and normal force balance gravity to maintain uniform circular motion on a conical incline, solving for the minimum coefficient of static friction in AP Physics 1.

Analyze uniform circular motion via a drum machine example, linking gravity, normal force, and centripetal acceleration for clothes on a rotating surface to estimate about 37.4 rotations per minute.

Explore Newton's universal law of gravitation, defining the attractive gravitational force as G m1 m2 / r^2. Relate to orbital motion and centripetal acceleration, illustrated by Earth–Moon dynamics.

Examine non-uniform circular motion by separating radial (centripetal) acceleration toward the center and tangential acceleration that changes speed, using v^2/r for centripetal and a car example.

Explore angular quantities that express position on a circle, linking arc length s = r theta to angular position theta, velocity omega, and acceleration alpha, and their motion equations.

Compute angular acceleration for a constant-acceleration rotation using delta theta and zero initial angular velocity, then relate time, angular velocity, and tangential speed to the radius.

Explore kinetic energy and gravitational potential energy, derive the kinetic energy formula, and explain how a falling object's potential energy converts into kinetic energy, illustrating conservation with m g h.

Use conservation of energy on a roller coaster, equating initial and final kinetic plus potential energy. Derive speeds at B, C, and D from height differences, with mass canceling.

Explore how work changes kinetic energy, distinguish external and internal forces, and apply the work-energy theorem with external work and gravitational potential energy in energy conservation.

Apply conservation of energy and work by external forces to solve motion with a coefficient of kinetic friction, using kinetic energy, gravitational potential energy, normal force, and centripetal acceleration.

Compute the scalar (dot) product by summing componentwise products and by using magnitudes and cosine of the angle between vectors. The lecture covers three‑dimensional and two‑dimensional cases with example vectors.

Explore how work depends on the angle between force and displacement using the dot product, with examples of positive, negative, and zero work.

Learn how spring force acts as a restoring force toward equilibrium, applying Hooke's law to calculate acceleration from displacement, spring constant, and mass in a 10 kg, 0.3 m setup.

Apply conservation of energy with spring and gravity potentials to find speed at equilibrium and maximum displacement, and then include friction to determine the travel distance to the lowest point.

Explore the difference between conservative and non-conservative forces, using gravity as conservative and friction as non-conservative, with work depending on path and potential energy applied only to conservative forces.

Power measures energy transferred per unit time, linking average and instantaneous power to work and energy; an elevator example shows power equals force times velocity in joules per second.

Explore momentum as mass times velocity, relate it to Newton's laws, and show net force as the derivative of momentum, with momentum conserved in isolated systems and three coalitions ahead.

Learn momentum conservation across elastic, perfectly inelastic, and inelastic collisions, with a two-block example where they stick and move together after impact, and energy loss calculation.

Explore momentum conservation across elastic, perfectly inelastic, and inelastic collisions with illustrative one- and two-dimensional examples. Learn how kinetic energy changes and final speeds follow from momentum and energy relations.

Apply conservation of momentum to calculate the cannon’s recoil speed after the bomb breaks away on a horizontal path. Show energy is not conserved.

Explore impulse as the change in momentum during collisions and apply Newton's laws to solve momentum problems. Use impulse formulas, net force concepts, and constant-force cases to analyze examples.

Apply conservation of energy and momentum to a 3 kg projectile breaking into 2 kg and 1 kg pieces. Use the kinetic energy change to find height and distance.

Explore conservation of momentum and energy through two pendulum-like balls that stick after collision, finding their maximum angle. Analyze a spring-block system with friction and energy transfer.

Apply conservation of energy to find the pendulum’s speed at the lowest point from the initial height L − L cos theta, then relate tension and gravity to centripetal acceleration.

Explore rotational dynamics, focusing on angular velocity, angular acceleration, and moment of inertia as resistance to change, including torque, angular momentum, and rotational kinetic energy.

Explore torque as the distance from the axis of rotation to the force, multiplied by force magnitude and sine theta, to determine angular acceleration and net torque.

Explore moment of inertia and rotational dynamics, applying torque equals I alpha to rigid bodies, including disk and rod, and solve pulley and two-mass rotation problems using kinematics.

Calculate the cross product of two vectors using component form to obtain a vector perpendicular to A and B; determine its magnitude and direction with the right-hand rule.

Use the cross product r × F to determine torque and the right-hand rule for direction, then compute x–y components for a 2 m radius and 200 N tangential force.

Explore rotational kinetic energy, using moment of inertia and angular velocity to calculate energy. Apply the conservation of energy and friction to stop a rotating wheel.

Explore angular momentum, its relation to moment of inertia and angular velocity, and conservation with no external torque, using I = m r^2 and L = I ω.

Apply angular momentum conservation to three examples—a figure skater, a wooden stake and ball, and a comet—using L = I ω to relate initial and final values.

Explore how angular momentum is a vector defined by L = r × p with p = mv, and compute it for a point mass about axis via cross product.

Explain the center of mass and how applying a force at the center yields equilibrium; show that linear and rotational motions can be treated independently in projectile and rotational motion.

This example links linear and rotational motion: use vertical projection of a 10 m/s throw at 45 degrees to find time, then compute angular displacement from angular velocity to revolutions.

Analyze a two-mass pulley system on an incline with a massive pulley, deriving accelerations and tensions via rotational dynamics, friction, and gravity.

Explore rotational dynamics with a pulley system of two masses and friction torque, solving for acceleration and time to ground, yielding a ≈ 1.61 m/s^2 and t ≈ 1.11 s.

Explore oscillatory motion and identify three key quantities - amplitude, period, and frequency - with real-world examples like a swing, guitar string, and mass-spring system.

Describe simple harmonic motion as an oscillation with a linear restoring force F = -k x, and derive x'' = -(k/n) x from Newton's second law.

Apply a trial solution x(t)=A cos(omega t+phi0) to simple harmonic motion and verify omega = sqrt(k/m); see how amplitude and phase shape initial conditions.

Review the simple harmonic motion equation and the solution x(t) = A cos(ωt+φ); note T = 2π/ω and ω = 2πf; initial conditions set amplitude and phase.

Derive displacement, velocity, and acceleration for simple harmonic motion using x = A cos(ωt+φ), v = -ωA sin(ωt+φ), and a = -ω^2 A cos(ωt+φ), including maxima.

Derive the simple pendulum’s equation of motion using tangential and radial forces; relate theta to arc length; show simple harmonic motion with frequency sqrt(g/L) and period 2 pi sqrt(L/g).

Examine energy in simple harmonic motion, showing conserved total energy from kinetic and potential components and derive velocity as a function of displacement.

We analyze a 3 cm amplitude simple harmonic motion example, using energy conservation to find the displacement where speed equals half of its maximum.

Use momentum conservation for the bullet and block inelastic collision, then energy conservation to find the maximum spring compression and the time to rest with ω = sqrt(K/(m+M)).

Explore a simple harmonic motion problem with a 0.2 kg block on a frictionless surface and a 200 N/m spring, deriving ω, frequency, period, phase constant, amplitude, and x(t).

Clarify how phase constant phi0 sets initial displacement and velocity in simple harmonic motion, linking angular frequency omega and time t to amplitude a, and show pi phase shifts.

Explore how uniform circular motion yields simple harmonic motion by deriving the x-displacement as the amplitude a times cosine of omega t plus phi naught.

Solve an example of harmonic motion: derive displacement x(t) as 0.02 cos(3π t + 3π/2), find max speed 0.9 m/s and max acceleration 1.78 m/s², 0.33 s and 0.167 s.

Explore vertical oscillations of a mass-spring system under gravity, derive the simple harmonic motion about the new equilibrium, and obtain the motion equation y(t) = A cos(ω t + φ0).