The Complete AP and College Physics Course

Explore kinematics by distinguishing distance from displacement, note that displacement is a vector, and define average speed as distance over time and average velocity as change in position over time.

Examine constant velocity and uniformly changing velocity on displacement-time and velocity-time graphs; derive instantaneous velocity as the tangent slope and displacement as the area under the velocity-time graph.

Apply the big five one dimensional motion formulas to free fall, deriving displacement under gravity with vertical coordinates.

Explore one-dimensional kinematics through practice exercises, applying the five big equations to analyze velocity, acceleration, displacement, and distance in varied AP physics problems.

Explore two-dimensional motion of a horizontally launched projectile with no air resistance, constant horizontal velocity and gravity causing vertical acceleration, yielding an inverted parabolic trajectory.

Define a force as a vector of push or pull with magnitude in newtons and a direction. Demonstrate net force and equilibrium by summing opposing forces to predict motion.

Explore how an object remains at rest or moves with constant velocity unless acted upon by a net external force, illustrating Newton's first law and the law of inertia.

Explain Newton's third law of motion, where every action has an equal and opposite reaction, as shown by the swimmer-wall push and rocket nozzle exhaust.

Define weight as the earth's gravitational force on a mass, not the mass itself. Use free body diagrams to show the normal force balancing weight in static equilibrium.

Decompose gravity on an object on an incline into parallel and perpendicular components, yielding mg sin theta and mg cos theta under no friction.

Explain static and kinetic friction, using mu_s, mu_k, and normal force mg, with F_s,max = mu_s mg, showing how a push overcomes static friction and invokes kinetic friction.

Analyze a mass on a string at an angle to vertical, decomposing tension into x and y components. Relate x component to centripetal force v^2/r and balance y with gravity.

Practice exercises applying Newton's laws to calculate net force, friction, tension, and acceleration across scenarios including incline planes, friction, and pulleys.

Compute work by taking the component of a 20 N force along the motion, F_w = F cos theta, and multiply by the 5 m distance to get W.

Explore the concept of energy, its forms, and how gravitational potential energy and kinetic energy arise as objects are lifted and fall, illustrating energy transfer and conservation.

Trace a pendulum's energy exchange from potential at the top to kinetic at the equilibrium, then back to potential as it rises, showing energy conservation and the role of velocity.

Apply the idea that energy is the ability to do work, and see how net work transfers energy to a body, increasing its kinetic energy, illustrating the work-energy theorem.

Explore core mechanics concepts through practice problems that connect kinetic energy, work, friction, and potential energy to real scenarios involving springs, gravity, and motion.

Define momentum as mass times velocity and show that for constant mass, net force equals the change in momentum over time, illustrating impulse.

On a frictionless pool table, a cue ball strikes the eight ball, and equal and opposite forces conserve total momentum, so the initial total momentum equals the final total momentum.

Explain the conservation of linear momentum in isolated, frictionless systems, and contrast elastic collisions that conserve kinetic energy with inelastic collisions that convert energy into heat and sound.

Torque measures how effectively a force causes rotation, linking to angular acceleration and rotational inertia, with positive values for counterclockwise motion and negative for clockwise rotation.

Define angular position theta and angular displacement as the change from initial to final position on a rotating wheel, using arc length L and radius R.

Balance two masses on a horizontal massless bar to achieve rotational equilibrium by equating torques: M1 g D = M2 g 3D, giving M2 = M1/3.

Define moment of inertia as the mass's resistance to rotation; derive I = m r^2 for a point mass and extend to bodies by summing m r^2.

Define angular momentum as the rotational analog of linear momentum, with L = I ω, and explain conservation when torque is near zero as radius changes, altering I and ω.

Practice exercises in rotational dynamics apply torque and moment of inertia to compute angular velocity, angular momentum, and angular acceleration in gears, levers, reels, and gyroscopes.

Derive gravitational potential energy and the escape velocity from Earth using conservation of energy, yielding v = sqrt(2GM/R) and noting near-Earth values around 11 km/s.

Derive the generalized gravitational potential energy in outer space by using calculus to relate the change in potential energy to work done by the inverse-square gravitational force.

Learn fluid mechanics basics, including fluid vs solid, density and pressure, and how atmospheric pressure adds to the pressure from a fluid's weight to determine total bottom pressure.

Pascal's principle states that pressure in an enclosed fluid is transmitted undiminished, so F1/A1 = F2/A2. A larger wheel cylinder area amplifies braking force in cars.

Archimedes principle states buoyant force equals the weight of displaced fluid; the submerged fraction equals the object's density divided by the fluid's density, linking density to floating or sinking.

Understand how a decrease in cross-sectional area raises velocity and kinetic energy. Link pressure changes along a streamline to Bernoulli's principle and note practical uses like nozzles and atomizers.