Vectors, Kinematics, and Newton's Laws: Study Guide and Syllabus Overview

Course Overview

This course covers foundational topics in Physics, focusing on vectors, kinematics in one and two dimensions, and Newton's Laws of Motion. The syllabus outlines weekly lessons, key concepts, and objectives, providing a structured approach to mastering the principles of motion and force.

Course Structure

Chapter Title	Lesson	Week	Other Resources
Chapter 1	Adding Vectors	Teams Week 2, Week 3	Worksheets, Practice sheets, PowerPoints, College board
Chapter 1	Multiplying Vectors	Teams Week 4	Worksheets, Practice sheets, PowerPoints, College board
Chapter 2	Motion in One Dimension – Graphical analysis	Teams Week 5	Worksheets, Practice sheets, PowerPoints, Quiz, College board
Chapter 2	Motion in One Dimension – Kinematics Equations, Free Fall	Teams Week 6	Worksheets, Practice sheets, Quiz, PowerPoints, College board
Chapter 2	Motion in Two Dimensions, Kinematics equations, Projectile Motion	Teams Week 7, Week 9	Worksheets, Practice sheets, PowerPoints, College board, Unit Test

Important Skills, Concepts, and Objectives

• Vectors:

  • Calculate the resultant vector graphically and algebraically.

  • Calculate the resultant of non-parallel vectors using vector and dot product.

  • Apply sine and cosine functions to determine the magnitude and direction of two-vector resultants.

  • Use the law of sines and cosines to add vectors.

  • Solve real-world problems using vector addition.

• Motion and Kinematics:

  • Define key concepts: distance, displacement, velocity, speed, and acceleration.

  • Deduce velocity and speed from displacement-time graphs.

  • Calculate displacement and acceleration from velocity-time graphs.

  • Apply kinematic equations to calculate velocity, acceleration, time, and displacement.

  • Apply kinematic equations to free fall and projectile motion (both horizontal and at an angle).

  • Describe motion in one and two dimensions.

• Newton's Laws of Motion:

  • Define force and explain Newton's 1st Law (Law of Inertia) and equilibrium.

  • Apply Newton's 2nd Law equations to solve for unknowns in force diagrams (FBDs).

  • Solve problems involving friction, tension, inclined planes, apparent weight, air resistance, Atwood machines, and pulleys.

Key Definitions and Formulas

Vectors

• Vector: A quantity with both magnitude and direction (e.g., displacement, velocity, force).

• Resultant Vector: The single vector that has the same effect as two or more vectors combined.

• Vector Addition (Graphical): Place vectors head-to-tail and draw the resultant from the start of the first to the end of the last.

• Vector Addition (Algebraic): For vectors $extbf{A}$ and $extbf{B}$: $\textbf{R} = \textbf{A} + \textbf{B}$

• Magnitude of a Vector: $|\textbf{A}| = \sqrt{A_x^2 + A_y^2}$

• Dot Product: $\textbf{A} \cdot \textbf{B} = |\textbf{A}| |\textbf{B}| \cos \theta$

• Law of Cosines: $c^2 = a^2 + b^2 - 2ab \cos \theta$

• Law of Sines: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Kinematics in One and Two Dimensions

• Displacement: $\Delta x = x_f - x_i$

• Average Velocity: $v_{avg} = \frac{\Delta x}{\Delta t}$

• Acceleration: $a = \frac{\Delta v}{\Delta t}$

• Kinematic Equations (constant acceleration):

  • $v = v_0 + at$

  • $x = x_0 + v_0 t + \frac{1}{2} a t^2$

  • $v^2 = v_0^2 + 2a(x - x_0)$

• Projectile Motion: Motion in two dimensions under gravity, with horizontal and vertical components analyzed separately.

Newton's Laws of Motion

• First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net external force.

• Second Law: $\sum F = ma$

• Third Law: For every action, there is an equal and opposite reaction.

• Free-Body Diagram (FBD): A diagram showing all forces acting on an object.

Assessment Structure

• 60% Multiple Choice Questions

• 40% Free Response Questions

• Total: 100 points

Additional Info

• All important concepts listed above can be tested.

• Students must bring their own stationery and calculators; no sharing is allowed.

• All exams will be on paper.