Essential physics : Master classical and Newtonian mechanics

Explore classical and Newtonian mechanics through nine chapters on units, vectors, one- and two-dimensional motion, circular motion, friction, Newton's laws, work, energy, momentum, collisions, and rotation.

Explore how measurements define physical quantities and enable meaningful comparison, compare the CGS, SI, and British engineering systems, and emphasize using consistent units and derived units in calculations.

Explore the conversion of units across prefixes, from grams and kilograms to centimeters and meters, practice area calculations, and relate density and metric tons to cubic meters.

Explore significant figures and measurement precision, and learn which digits are significant in numbers. Apply rounding rules for addition, subtraction, multiplication, and division using the least precise measurement.

Explore scientific notation for expressing very large or very small numbers with powers of ten, using positive or negative exponents, illustrated by the speed of light in vacuum and 5.492×10^3.

Use right-triangle trigonometry to find theta and phi from sides a and b (2.5 m and 6 m) and compute the hypotenuse c, applying sine, tangent, and angle relationships.

Explore coordinate systems in physics, focusing on Cartesian coordinates and plane polar coordinates to describe object positions, vectors, and kinematics in two dimensions.

Explore vectors and scalars, understanding magnitude and direction, how to add or subtract vectors, and represent them with arrows and Cartesian components in motion analysis.

Explore how to add and subtract vectors with graphical and component methods, construct the resultant, and determine its magnitude and direction from x and y components.

Define displacement, average velocity, velocity, and acceleration in one dimension, and establish the basic equations of motion and their relationships within coordinate systems.

Displacement is the change in position along the x axis in one dimension, computed as x_f minus x_i, a vector with magnitude and direction that can be eastward or westward.

Learn how average velocity, defined as displacement over a time interval, describes an object's overall motion between two positions, with velocity as a vector.

Learn how to compute average speed and average velocity from displacement and distance, using time intervals for forward, backward, and round-trip motion, with practical examples.

Instantaneous velocity is the slope of the tangent to the velocity curve at a point, computed as rise over run. It contrasts with average velocity, delta x over delta t.

Explore how acceleration results from velocity changes over time, distinguishing average and instantaneous acceleration and applying the equation of motion v0 + a t.

Explore the equations of motion with constant acceleration, linking velocity and displacement, including v^2 = v0^2 + 2ax, using a braking example.

Explore vertical motion under constant earth gravity with downward acceleration, using upward-positive y and origin at start, to compute time to max height and impact velocity.

Resolve displacement, velocity, and acceleration into x and y components in a two-dimensional plane using Cartesian coordinates. Treat each component separately to simplify motion analysis, with time governing both directions.

Explore two-dimensional motion by resolving displacement into x and y components, defining average and instantaneous velocities, and analyzing ax and ay for constant acceleration with practical examples.

Two independent sets of equations describe motion in the x and y directions. Setting the origin at the initial position allows solving these for the object's x and y positions.

Master projectile motion as two-dimensional motion under gravity, with x-velocity constant and y-acceleration -g. Resolve initial velocity into x and y components to compute time of flight, height, and range.

Explore uniform circular motion: a body rotates in a fixed circle at constant speed, with centripetal acceleration toward the center, a_c = v^2 / r, where v is tangential velocity.

Explore circular motion fundamentals by deriving period, linear and angular velocity, and frequency, then apply v = omega r to calculate centripetal acceleration for rotating objects.

Explain nonuniform circular motion by separating total acceleration into centripetal and tangential components, show how changing speed adds a tangential acceleration, with a practical racing car example.

Learn how forces create acceleration and change velocity, explore kinematics and dynamics, and apply Newton's laws to linear and circular motion.

Newton's laws of motion are presented: objects stay at rest or in uniform motion unless acted on; net force equals mass times acceleration; action and reaction are equal and opposite.

Explore how Newton's laws connect net force, momentum, and acceleration, showing zero net force keeps momentum and velocity constant, and derive F = dp/dt and F = m a.

Isolate the object and draw its free body diagram showing weight mg, normal force, and friction, then apply Newton's second law to obtain acceleration and net force.

Note acceleration follows the net force, the larger one when two oppose; resolve forces into x and y components and apply Newton's second law to each, with forces as arrows.

Explore how two masses attract under Newton's third law, and apply the inverse-square law F = G m1 m2 / r^2 to reach near earth g ≈ 9.8 m/s^2.

Mass is constant and measured in kilograms, while weight is the gravitational force that varies by location; W = m*g with g differing on Earth, Moon, and Mars.

Explain how apparent weight equals the normal force on a scale, increasing with upward elevator acceleration and decreasing with downward acceleration, per Newton's second law.

Explore centripetal acceleration and the net centripetal force that sustains uniform circular motion, with examples of a mass on a string and curved-road motion under frictionless conditions.

Apply Newton's laws to friction and other forces in linear and circular motion. Explore how resistive forces like air resistance interact with elastic and gravitational forces.

Explore frictional forces in linear and circular motion, distinguishing static and kinetic friction and their coefficients, and analyze the normal force and centripetal requirements in curves.

Apply Newton's laws to moving objects by detailing forces, then use energy methods based on work and kinetic energy. Define potential energy, conservative forces like gravity, and total mechanical energy.

Explore how work equals force times displacement times cosine of the angle between them, showing zero work when force is perpendicular to displacement and nonzero otherwise.

Derive the work-energy theorem from Newton's laws, linking net work to the change in kinetic energy. Illustrate with frictionless motion and gravity to find height and speed.

Explore how conservative forces like gravity and spring forces yield zero net work on a closed path, keeping kinetic energy unchanged after a round trip, unlike dissipative non-conservative forces.

This lecture defines potential energy and explains how, via the work-energy theorem, conservative forces transfer energy between kinetic and potential forms, keeping mechanical energy constant with gravity and springs.

Explore how the work-energy theorem splits into conservative and non-conservative work, linking changes in kinetic and potential energy to the total mechanical energy and showing non-conservative forces dissipate energy.

learn how power measures the time rate of work, with average power as work per time and instantaneous power as force times velocity; units include watt and kilowatt.

Explore linear momentum for a single object and for systems, define the center of mass, and apply Newton's laws to colliding bodies, focusing on the short contact forces during collision.

Compute the center of mass for a discrete particle system by weighting positions with mass and dividing by the total mass, as shown in two-mass and square examples.

Move with the center of mass under external forces, derive its x and y displacements and velocities, and treat the system as a single mass obeying Newton’s second law.

Explore how a system's linear momentum equals the sum of all particles' momenta and the center-of-mass velocity. A zero external force keeps momentum constant, underpinning conservation in two dimensional collisions.

Conserve linear momentum in collisions by equating the change in momentum to the force times collision time, with equal and opposite forces and no external forces.

Define impulse as the change in momentum, J = F Δt, and show how equal and opposite impulses conserve total momentum in a system, illustrated by a bullet and gun.

Explore how linear momentum is conserved in two-dimensional collisions, decompose vector equations into x and y components, and solve for fragment velocities and directions in a multi-fragment explosion example.

Explore elastic and inelastic collisions by applying conservation of momentum and kinetic energy, illustrated with a one-dimensional two-object collision and energy changes.

Explore rotational motion by examining rigid bodies (extended objects) rotating about fixed axes or their center of mass, and study their translation and rotation.

Explore angular kinematic quantities, linking arc length to radius and angle, deriving velocity equals radius times omega and angular velocity equals change in angle over time, with constant angular acceleration.

Explore rotational motion in a plane through angular velocity, angular acceleration, the link between linear and angular quantities, and arc length, with practical unit conversions.

Define torque as force times the lever arm’s perpendicular distance to the axis and relate it to angular acceleration through the moment of inertia, using x, y, and z axes.

Explore rigid bodies by extending the point-particle approach to systems of discrete objects bound together, or to objects with finite continuous mass distributions, defined as rigid bodies.

Explore how the moment of inertia defines a system's resistance to rotation about an axis, for discrete masses and continuous distributions, and see how axis location changes its value.

The parallel axis theorem links a rigid body's moment of inertia about an axis parallel to the center of mass to their separation, useful for rolling cylinders or spheres.

Apply equilibrium to a rigid body by making the net force and net torque zero, using force components and torque about a point, illustrated with a meter stick.

Discover how angular momentum equals moment of inertia times angular velocity, how torque changes it, and how conservation arises, illustrated by rotating slab and disk examples.

Examine rotational kinetic energy in classical mechanics, linking translational energy to rotation with v = ωr, I = mr^2, and KE = 1/2 I ω^2 for a rigid body.

Demonstrate that a rigid body's total kinetic energy equals the sum of translational energy of the center of mass and rotational energy about it, for discrete particles or continuous mass.

Apply the conservation of mechanical energy to frictionless and conservative forces problems to derive velocities for a pulley system with two masses and a solid sphere rolling down an incline.