Newton's Three Laws of Motion

• Force ($\vec{F}$): A vector quantity representing a push or pull upon an object resulting from its interaction with another object. It is measured in Newtons (N), where $1\text{ N} = 1\text{ kg} \cdot \text{m/s}^2$.

• Mass ($m$): A scalar measure of an object's resistance to acceleration (inertia) and the amount of matter it contains. Unlike weight, mass remains constant regardless of gravitational environment.

• Acceleration ($\vec{a}$): The rate of change of velocity over time. It occurs whenever an object speeds up, slows down, or changes direction.

• Net Force ($\sum \vec{F}$): The vector sum of all individual forces acting on an isolated system. Only a non-zero net force can change an object's state of motion.

• The Mathematical Relationship: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Fundamental Formula: $\sum \vec{F} = m\vec{a}$

• Directionality: The acceleration vector always points in the same direction as the net force vector. If multiple forces act on an object, they must be resolved into components (usually $x$ and $y$) to find the resultant acceleration.

• Application: This law is used to calculate the required force to achieve a specific motion or to predict the resulting motion when forces are known.

Mass vs. Weight

• Mass is an intrinsic property representing the quantity of matter ($kg$), while Weight is the force of gravity acting on that mass ($N$).
• Weight is calculated as $W = mg$, where $g$ is the local gravitational acceleration.

Balanced vs. Unbalanced Forces

• Free Body Diagrams (FBD): Always start by drawing an FBD. Isolate the object of interest and draw all external forces acting on it. Never include forces the object exerts on others in its own FBD.

• Coordinate Systems: Choose a coordinate system that aligns with the expected direction of motion. This simplifies the vector decomposition of forces into $x$ and $y$ components.

• Check Units: Ensure mass is in kilograms and acceleration is in $m/s^2$ before calculating force in Newtons. A common error is using grams or centimeters.

• The 'Constant Velocity' Trap: If an exam question states an object is moving at a 'constant speed' or 'constant velocity', immediately set the net force to zero. Students often mistakenly try to calculate a net force for moving objects even when they aren't accelerating.