Mechanics

Introduction to Mechanics

Mechanics is the branch of physics concerned with the study of motion and the forces that cause or change motion. It forms the foundation for understanding a wide range of physical phenomena, from everyday experiences to microscopic processes.

• Definition: Mechanics is the study of motion and its causes.

• Applications: Motion of microscopic particles underlies phenomena such as fluid flow, diffusion, heat conduction, and cell membrane processes.

• Intuition: Everyday experience provides basic intuition for motion, but mechanics formalizes this understanding mathematically.

Organizing Mechanics

Main Subfields of Mechanics

Mechanics is typically divided into three main areas, each addressing different aspects of motion and its causes.

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

• Interactions (Force and Torque): How do objects interact, and what causes or changes motion?

• Energy: What is energy, and how do energy transfers and transformations inform us about 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 represented by a single point, ignoring its size and shape, which allows us to focus solely on its position in space.

• Key Point: The motion of an object is described by tracking a single point on the object.

• Example: A tennis ball can be modeled as a point particle when analyzing its trajectory.

Measuring Motion

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

• Coordinate System: A framework for specifying the position of objects in space.

• Choices:

  • Location of the origin (zero point)

  • Orientation of axes in space

  • Direction assigned as positive or negative along each axis

  • Reference time set as

Coordinate Systems

One-Dimensional Motion

If an object moves along a straight line, only one coordinate axis is needed to describe its position. This is called one-dimensional motion.

• Example: A person running along a track can be described using the x-axis alone.

Two-Dimensional Motion

If an object moves in a plane, such as a ball rolling on a table, two axes (x and y) are required. This is called two-dimensional motion.

• Example: The position of a ball on a tabletop is described by both x and y coordinates.

Units

Standard System of Units

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

• Unit of time: Second (s)

• Unit of distance: Meter (m) (1.0 m ≈ 3.3 feet)

Scientific Notation

Large and small values are often represented using scientific notation, which expresses numbers as multiples of powers of ten.

• Example: The average Earth-Sun distance is m, written as m in scientific notation.

SI Unit Prefixes

Common SI Prefixes

SI prefixes are used to simplify the expression of very large or very small quantities. Each prefix represents a specific power of ten.

• Example: The diameter of an E. coli bacterium is m, or .

Significant Digits

Understanding Significant Figures

Significant digits (or significant figures, "sig figs") are a simplified way to express the uncertainty in physical measurements. They indicate the precision of a measured or calculated value.

• Rule of Thumb: Answers should have the same number of significant digits as the numbers provided in the problem.

• Example: If lengths are given as 2.0 m and 3.0 m, the area should be reported as 6.0 m2, not 6 m2.

Additional info: Significant figures are important in laboratory and experimental physics to communicate the reliability of measurements and calculations.