Physics 12: Classical Mechanics

Solve for the position of an object in uniform motion by applying the definition of velocity as instantaneous at any given time, recognizing constant velocity in uniform motion.

Explore the equation of motion for an object moving on a straight x-axis, deriving position, velocity, and acceleration from a given relation and calculating average velocity and x-values.

Explore the velocity–position relation in uniformly accelerated motion, showing how constant acceleration with initial position and velocity governs motion and how x and y components relate.

Analyze a one-dimensional relative motion problem with two objects moving at constant speeds along a line; set the car as origin and solve for the meeting time when x1(t)=x2(t).

Balance the forces on an object of mass at rest on an incline by resolving gravity into components along and perpendicular to the plane, using normal force and static friction.

Analyze a classical mechanics problem about an elevator with upward constant acceleration and a person inside, using sign conventions to determine the direction and magnitude of the net acceleration.

Analyze a mass on a 30-degree incline with kinetic friction mu_k = 0.2 at constant velocity to determine the tension by balancing gravity, normal force, and friction along the incline.

Analyze a two-object system on a table connected by a string, with gravity, normal force, and tension, to determine the net force and common acceleration via Newton's laws.

Explore kinetic energy and its relation to an object's mass and motion, and describe potential energy arising from position relative to other objects.

Explore how net forces relate to work and how gravitational potential energy changes with position, linking force, energy, and motion.

Explore mechanical energy, the sum of kinetic and potential energy, and its conservation in a system. Relate changes in kinetic energy to changes in potential energy.

Examine how elastic potential energy stores energy in a perfectly elastic spring, as work from a nonconstant force leads to e_p = 1/2 k x^2 for extension x.

solves a classical mechanics problem by applying net force equals mass times acceleration, including gravity and tension, and uses work and kinetic energy change to determine motion.

Analyze a projectile problem by tracking kinetic and potential energy, showing initial mechanical energy equals kinetic plus potential, with ground-level energy and discussion of energy dissipation.

Explore the work-energy theorem by linking net force to acceleration and velocity, showing that work equals the change in kinetic energy as an object moves from initial to final position.

analyze a 2.5 kg mass on a spring under gravity. apply energy conservation to relate kinetic energy to elastic potential energy as energy transfers within the system.

conservation of linear momentum shows that, with zero external forces, the total momentum before collision equals after, due to action–reaction impulses.

Explore elastic and inelastic collisions, showing how conservation of kinetic energy and momentum governs two-particle interactions from initial to final states.

Explore a straight-line car crash scenario to compute the average force acting on the car as it crashes into a barrier.

Apply conservation of momentum and kinetic energy to a two-ball elastic collision, resolving initial velocities into x and y components and calculating final speeds.

Use momentum conservation to analyze a two-car collision that locks together, compute final velocities, and quantify kinetic energy loss—about 52.4% of the initial energy is lost.

Explore the relation between kinetic energy and gravitational potential energy in a mass-based system, with gravity g ≈ 9.8 m/s² and energy transfer during motion and collisions.

Explore oscillation and periodic motion, including simple harmonic motion around a stable equilibrium. Learn how period and frequency quantify cycle duration and cycles per unit time.

Learn the equation of motion for a simple harmonic oscillator and how to determine its period. Analyze how kinetic and potential energy exchange throughout the motion.

Solve a centripetal force problem for a 0.455 kg object on a string and determine the maximum speed before the tension reaches a 400-ton limit, using the radius.

Illustrates a 484 g mass in vertical circular motion, showing gravity and tension as centripetal forces and solving for radius, speed, and the related energy terms in the string setup.

Analyze a car’s motion on a curved path using a two-dimensional x and y coordinate system, identifying the centripetal force and the role of gravitational force with cosine components.

Learn Newton's law of universal gravitation: two masses attract along the line joining them with a force proportional to the product of their masses and inversely to the distance squared.

Examine how gravitational, electric, and magnetic fields act as forces in space, define gravitational field intensity g, and apply Newton’s universal gravitation with inverse-square dependence and direction toward masses.

Analyze how a satellite, under Earth's gravity as the sole force, follows uniform circular motion with a constant centripetal force provided by gravity, described by the universal constant G.

Explore how gravitational pull between earth and moon depends on mass and distance, using F = G m1 m2 / r^2 and the gravitational field, solved via a quadratic approach.

Tackle a problem involving the gravitational field on a planet, analyze mass, and explore how alignment and reasoning lead to a solution in classical mechanics.

Solve a classical mechanics problem involving the gravitational field and mass, deriving related equations and applying the solution to determine key quantities.