Author Capstone Axis

Aristotle’s Fallacy Aristotle believed an external force is needed to keep a body in motion. For example, he thought air pushes an arrow forward after it’s shot. This idea seems intuitive because everyday objects (like toy cars) stop moving without external force. However, Aristotle overlooked friction as the opposing force. In reality: Objects slow down […]

Chapter 4: Laws of Motion 4.1 Introduction Key Idea: Forces are needed to change an object’s motion. Let’s break this down! 💡 Force & Motion: To move a stationary object (like a football), you need a force (e.g., a kick). To stop a moving object (like a rolling ball), you also need a force acting

Uniform Circular Motion When an object moves along a circular path at a constant speed, it’s called uniform circular motion. Even though the speed is constant, the object accelerates because its direction of motion keeps changing! Key Concepts Centripetal Acceleration: The acceleration is always directed toward the center of the circle. Its magnitude is: \(

Projectile Motion Notes Equations of Motion Position as a function of time: \[ r = r_0 + v_0 t + \frac{1}{2} a t^2 \] Break into x and y components: \[ x = x_0 + v_{0x} t + \frac{1}{2} a_x t^2 \] \[ y = y_0 + v_{0y} t + \frac{1}{2} a_y t^2 \] Horizontal

Understanding Motion in 2D When an object moves in a plane (like the x-y plane), its velocity and acceleration can point in different directions. Unlike 1D motion, here, velocity (\( \vec{v} \)) and acceleration (\( \vec{a} \)) can form any angle between them! Key Equations for Constant Acceleration Velocity-Time Relation: \( \vec{v} = \vec{v}_0 +

Vector Addition in a Plane When two vectors A and B act at an angle θ, their resultant R can be found using the parallelogram method: Magnitude of R: \[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \] (Law of Cosines) Direction of R (angle α with vector A): \[ \tan \alpha =

Vector Addition — The Component (Analytical) Method When you break every vector into x– and y-components, adding vectors feels just like adding ordinary numbers. Here’s the step-by-step story. 1. Writing a vector as components For a vector in the plane we write \[ \mathbf A = A_x \,\hat{\mathbf i} + A_y \,\hat{\mathbf j} \] so

Resolution of Vectors — Quick, Friendly Notes Whenever you break a single vector into parts or put several vectors together, you’re “resolving” or “adding” them. These notes walk you through the key ideas step-by-step, using easy language and plenty of examples. 1 · Why Resolve a Vector? Imagine sliding a heavy box: it’s easier to think of

Vector Addition and Subtraction: Graphical Methods 1. Adding Vectors Head-to-Tail (Triangle) Method: Place the tail of vector B at the head of vector A. Draw a line from the tail of A to the head of B. This line is the resultant R = A + B. Parallelogram Method: Bring both vectors A and B

Multiplication of Vectors by Real Numbers Key Concepts When you multiply a vector 𝐀 by a positive number λ, the direction stays the same, but the magnitude (length) changes by a factor of λ: |λ𝐀| = λ|𝐀| (if λ > 0). Example: Doubling vector 𝐀 gives 2𝐀, which is twice as long but points the