Mechanics

Introduction to Mechanics

Mechanics is the branch of physics concerned with the study of motion. Understanding mechanics is fundamental because it underlies many phenomena in both everyday life and scientific contexts, such as fluid flow, diffusion, and heat conduction.

• Mechanics studies how and why objects move.

• Everyday intuition about motion is formalized and extended in physics.

• The motion of microscopic particles is crucial for understanding processes in biology, chemistry, and engineering.

Organizing Mechanics

Main Subfields of Mechanics

Mechanics can be organized into three main areas, each addressing a different aspect of motion:

• Kinematics (Representing Motion): How do we describe and represent motion mathematically?

• Dynamics (Forces and Torques): How do objects interact, and what causes or changes motion?

• Energy: What is energy, and how do energy transfers and transformations relate to motion?

Representing Motion

Point Particle Model

To simplify the study of motion, we often use the point particle model. In this model, an object is treated as if all its mass is concentrated at a single point, allowing us to focus on its position in space without considering its size or shape.

• Only the position of a single point on the object is tracked.

• This model is valid when the object's size is negligible compared to the distances it moves.

Measuring Motion and Coordinate Systems

To describe motion quantitatively, we need to measure distance and position. This requires choosing a coordinate system, which is a set of axes and an origin for reference.

• The choice of coordinate system is arbitrary, but once chosen, all measurements must be consistent with it.

• Physical laws are independent of the coordinate system, but numerical values depend on the chosen axes and origin.

Key Choices in Setting Up a Coordinate System

• Where is the origin (zero point) of the axes?

• How are the axes oriented in space?

• Which direction is positive or negative along each axis?

• What time is set as t = 0?

Types of Motion

• One-dimensional motion: Motion along a straight line (e.g., a runner on a track) can be described with a single coordinate axis (usually x).

• Two-dimensional motion: Motion in a plane (e.g., a ball rolling on a table) requires two axes (x and y).

Units and Measurement

Standard Units in Physics

Physics uses a standard system of units to ensure consistency and comparability of measurements. The most common system is the International System of Units (SI).

• Unit of time: second (s)

• Unit of distance: meter (m) — 1.0 m is approximately 3.3 feet

Scientific Notation

Large and small values are often represented using scientific notation, which expresses numbers as a product of a coefficient and a power of ten.

• Example: The average Earth-Sun distance is m.

SI Unit Prefixes

SI prefixes are used to simplify the expression of very large or very small quantities by denoting powers of ten.

• Example:

Significant Digits

Significant digits (or significant figures, "sig figs") are a simplified way to express the uncertainty in physical measurements.

• As a rule of thumb, the answer to a calculation should have the same number of significant digits as the least precise number used in the calculation.

• Example: The area of a rectangle with lengths 2.0 m and 3.0 m is 6.0 m2 (not 6 m2).

Additional info: Later lectures will build on these foundations to introduce vectors, velocity, acceleration, and more advanced kinematic concepts.