Representing Motion

Point particles

A point mass is a theoretical concept in physics where an object is assumed to be mass concentrated at a single, infinitesimally small point. This model simplifies analysis by ignoring the object's size and shape, focusing solely on its mass. Similarly, a point charge is an idealized model of a charged particle where the charge is concentrated at a single point, disregarding the size and spatial distribution of the charge. These models are essential in studying mechanics and electromagnetism, simplifying complex calculations while providing significant insights.

Reference frames

A reference frame consists of an object of reference, a point of reference on that object, a coordinate system whose origin is at the point of reference, and a clock.

This course uses Cartesian coordinates (using x, y, and z axes). In two dimensions, the Cartesian system divides the plane into four quadrants. Each quadrant corresponds to a unique combination of positive and negative values along the x (horizontal) and y (vertical) axes. In addition to quadrants, directions like North (N), South (S), East (E), and West (W) are commonly used in geographic and navigational contexts.

Vectors

Vectors are quantities that have both a magnitude and a direction. Examples include displacement, velocity, acceleration, force, and momentum. Vectors are typically represented by arrows. Here's how:

Length of the Arrow: The magnitude of the vector is shown by the length of the arrow. A scale is chosen where a certain length of the arrow represents a certain magnitude of the vector quantity.
Direction of the Arrow: The direction of the vector is indicated by the direction in which the arrow points. The arrowhead points in the direction that the vector is acting.
Line of Action: The line on which the arrow lies is the line of action of the vector, and it's important when considering vector quantities in physics, especially in equilibrium problems and vector addition.

Motion Graphs

Graphing motion is a fundamental aspect of understanding physics and how objects move in space and time. Here are some key points to consider when graphing motion:

Slope and Area:

On a position-time graph, the slope gives the velocity.
On a velocity-time graph, the slope gives the acceleration, and the area under the curve between two points in time gives the change in position (displacement).

Curved Lines:

A curved line on a position-time graph indicates changing velocity — acceleration or deceleration.
A curved line on a velocity-time graph suggests changing acceleration.

Direction:

In one-dimensional motion graphs, the direction of motion can be indicated by the sign of the slope. Positive slope indicates motion in one direction, while a negative slope indicates motion in the opposite direction.

Graphical Integration and Differentiation:

In the context of motion graphs, differentiating the position with respect to time gives you the velocity, and differentiating velocity with respect to time gives you acceleration.
Conversely, integrating acceleration over time gives you velocity, and integrating velocity over time gives you position.

Source: Motion Graphs (Hyperphysics)

Dot / Motion Diagrams

Dot diagrams, also known as ticker-tape diagrams or motion diagrams, are a simple yet powerful way to describe motion in physics.

Drawing Dot Diagrams: Draw dots to represent the position of the object with respect to the observer at equal time intervals. Point velocity vector arrows in the direction of the motion and draw their relative lengths to indicate approximately how fast the object is moving.

Distance Between Dots: The spacing between the dots indicates the object’s speed. If the dots are far apart, the object is moving quickly; if they’re close together, it’s moving slowly. Uniform spacing indicates constant speed.

Velocity change arrow: You can draw velocity change arrows to indicate how the velocity arrows are changinging between positions.

View Demo

Correspondence between a motion diagram and position-time graph:

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