Classical Mechanics for High School Students

Embark on a comprehensive journey through classical mechanics, starting with vector algebra and kinematics, exploring rectilinear and projectile motion, then introducing Newtonian mechanics and finally Lagrangian and Hamiltonian frameworks.

Define physical quantities as measurable, distinguish scalars from vectors, note that vectors have magnitude and direction while scalars have magnitude only, and that weight is not a scalar.

Represent a vector as an arrow with a head and tail, show magnitude by length, and denote it as A with an arrow or boldface.

Learn to express a vector by its magnitude and direction, define unit vectors, and write any vector as the product of its magnitude and a direction unit vector.

Learn vector algebra basics, including unit vectors formed by dividing by magnitude, and key terms: null, equal, parallel and unlike parallel, collinear, and coplanar vectors.

Learn to add two vectors using the triangle law, joining heads and tails to form a resultant, and determine its magnitude via the angle between vectors.

Apply the parallelogram law to add two vectors, using the diagonal as the resultant, extend to the polygonal law for multiple vectors, and learn subtraction by taking a vector's negative.

Explore scalar multiplication by a real number, showing how vectors scale in magnitude and retain or reverse direction, and distinguish free versus bound vectors and the triangle law.

Learn to express vectors in Cartesian coordinates using i cap, j cap, and k cap, and represent points by x, y, z components in two and three dimensions.

Add vectors using unit vectors i hat, j hat, k hat by adding coefficients in the general form a i hat + b j hat + c k hat.

Explore how unit vectors simplify vector addition by adding components separately, forming a resultant along the x and y directions, illustrated with i and j components and parallelogram diagrams.

Define the position vector as the origin-to-point vector in Cartesian coordinates, and use Pythagoras to find its magnitude as 5 for (3,4) and the unit vector (3/5, 4/5).

Resolve a vector into its components using unit vectors i, j, k in two and three dimensions, applying cos alpha, cos beta, cos gamma and practical examples.

Explore vector addition in parallelograms, derive ac plus bd equals two times bc, and with midpoints e and f on bc and cd, show ae plus af equals 3/2 ac.

explores dot product and scalar product of two vectors, showing how magnitude and angle govern the result, with projection interpretations and unit vector references i, j, k.

Define the cross product as |a||b|sinθ n̂ and apply the right-hand thumb rule to find direction; use determinants for i, j, k and note distributive and anti-commutative properties.

Solve five vector problems using A and B directions, unit vectors, dot and cross products, and vector resolution into components with magnitudes and trigonometric angles.