Significant Digits (Sig Figs)

Definition and Rules

• Significant digits (sig figs) indicate the precision of a measured or calculated quantity.

• Scientific notation:

• Only 1 digit in front of the decimal is allowed in scientific notation.

• The number of significant digits is determined by the number of digits reported, not by the exponent.

Conversions

Common Unit Conversions

• 1 km = 1000 m

• 1 m = 100 cm

• 1 cm = 10 mm

Uniform Motion vs. Non-Uniform Motion

Graphical Representation

• Uniform motion: Object moves at a constant speed in a straight line.

• Non-uniform motion: Object's speed or direction changes over time.

• Graphs can help distinguish between these types of motion (e.g., position vs. time graphs).

Scalars vs. Vectors

Definitions and Examples

• Scalar: Magnitude only (e.g., distance, speed, mass).

• Vector: Magnitude and direction (e.g., displacement, velocity, acceleration).

Distance vs. Displacement; Speed vs. Velocity; Acceleration

Key Quantities and Equations

• Distance: Total path length traveled (scalar).

• Displacement: Straight-line change in position (vector).

• Speed: (scalar).

• Velocity: (vector).

• Acceleration: (vector).

Graphical Analysis

• Position vs. Time: Slope gives velocity.

• Velocity vs. Time: Slope gives acceleration; area under curve gives displacement.

• Acceleration vs. Time: Area under curve gives change in velocity.

Work

Definition and Formula

• Work (): The energy transferred when a force acts over a distance.

• = force (N), = displacement (m)

Force & Weight

Newton's Second Law and Weight

• Force:

• Weight:

• = acceleration due to gravity

Potential Energy

Gravitational Potential Energy

• Energy due to position in a gravitational field.

• = mass (kg), = , = height (m)

Kinetic Energy

Energy of Motion

• Energy due to motion, depends on mass and speed.

• = mass (kg), = speed (m/s)

Mechanical Energy

Sum of Kinetic and Potential Energy

• Total mechanical energy:

Law of Conservation of Energy

Principle

• Energy cannot be created or destroyed, only converted from one form to another.

• In a closed system, total mechanical energy remains constant (if no non-conservative forces act).

Thermodynamics

First Law of Thermodynamics

• Energy is conserved; energy input equals the sum of work done and change in internal energy.

Useful Energy & Efficiency

Efficiency Formula

• Efficiency measures how much input energy is converted to useful output.

• Can be calculated for energy or work, as long as units are consistent.

Types of Potential Energy

• Chemical, Elastic, and Nuclear energy are other forms of potential energy.

Summary Table: Kinematic Quantities

Additional info: Some context and explanations were expanded for clarity and completeness, including definitions, formulas, and the summary table.