Newton's Laws

Newton's First Law (Law of Inertia)

If there is no net external force on an object, the object does not accelerate (a = 0) and its velocity remains constant (velocity is a vector, so both speed and direction).
Constant speed does not imply no acceleration: circular motion has centripetal acceleration even though speed is constant because direction changes.
Mass is a measure of an object's linear inertia: inertia is the resistance to a change in velocity.
Inertia is not a force.

Mass, Inertia, and Weight

Mass (M) is a measure of inertia (the tendency to keep moving at constant velocity).
Weight (force due to gravity) is a force, not mass.
Gravitational force on an object near Earth’s surface is downward.
g is a positive constant (near Earth’s surface).

Newton's Second Law

Net force equals mass times acceleration.
Component form involves summing forces in x and y directions to relate to mass and acceleration components.
Units: Force is the Newton.

Forces to Identify (Free-Body Forces)

Force of gravity (weight): downward.
Push or pull (applied force).
Tension: force from a rope/cord; points away from the object along the rope.- Along a single rope, the tension magnitude is the same at all points; no pulleys considered yet.
Friction: contact force opposing motion (to be covered in a separate video).
Normal force (contact force): perpendicular to the surface
Scale reading equals the normal force (the contact force that the surface exerts on you).

Normal Force and Free-Body Diagrams

Normal force is perpendicular to contact surfaces (e.g., block on a ramp: is perpendicular to the ramp).
When analyzing a problem, list all forces acting on the object to compute the net force.

Quick Concept Checks

Weight vs mass:
- Weight is a force.
- Mass is a measure of inertia (not a force).
Velocity vs speed:
- Velocity is a vector; constant speed does not guarantee zero acceleration (direction change, e.g., circular motion).

Worked Notes for Problem Solving

Net force on an object (per Newton's 2nd Law) is the sum of all individual forces on that object.
Use components when solving multi-dimensional problems.

Free Body Diagram Essentials for Newton's Laws

Free Body Diagram Basics

Purpose: apply Newton's second law to a single isolated object.
Isolate the object: remove surroundings; draw the mass only.
Draw individual forces on that mass: gravity, normal, friction if present; direction arrows; try to scale roughly if possible.

Forces to include (examples):

Forces not to include:

Solve step:

Determine if acceleration is zero or not; label acceleration near but not on the diagram as a double-headed arrow if nonzero.
If acceleration is zero, write "a = 0" near the diagram instead of an arrow.

Axis placement:

Draw axes near but not on the diagram.
Can tilt axes: choose one axis parallel to direction of motion, e.g., along the ramp; or perpendicular to ramp if convenient.
You can choose which direction is positive (e.g., positive x down ramp).

Example: box on a ramp

Forces: Gravity downward; Normal force perpendicular to ramp; friction if present along ramp.
Acceleration will be along ramp if no friction.

Example: box in an elevator

Net force vs. forces:

The net force is the vector sum of the individual forces; it is not drawn on the FBD.
Net force will be used in subsequent steps to find acceleration.

Quick recap rules:

Problem-solving checklist

Is object isolated?
Is the mass clearly drawn?
Are all actual forces on the object included?
Are acceleration arrows placed near but not on the diagram?
Are axes defined, possibly tilted, and consistent with chosen positive directions?
Is the net force computed in later steps, not drawn on the diagram?

Newton's Third Law

Core Concept of Newton's Third Law: For every force that object 1 exerts on object 2, object 2 exerts an equal magnitude but opposite direction force on object 1. The pair is called the Newton's third law pair or action-reaction pair; forces are of the same type.

Key Features of a Third-Law Pair

F{12} acts on object 2; F{21} acts on object 1 (different objects).
Magnitude equal and directions opposite.
Forces in the pair are the same type (e.g., both pushes, both friction, both gravity, etc.).

Common Misconceptions

Common misconception: weight and normal force are Newton's third law pairs. Not true.
Weight on the box: Earth pulls on the box downward; the pair of this force is the box pulling on the Earth upward.
Normal force on the box from the table: table pushes up on the box; the pair is the box pushing down on the table.
Important: Newton's third law pairs must act on different objects and be the same type; equal and opposite forces on the same object are not a third-law pair.
Correct contrasts:
- Gravity pair: Earth on Box (gravity) vs Box on Earth (gravity).
- Normal-force pair: Table on Box (normal force) vs Box on Table (normal force).

How to Identify Newton's Third Law Pairs

Identify the force type (gravity, normal, friction, push, tension, etc.).
Determine the source object causing the force.
Determine the object experiencing the force.
Check that the two forces act on different objects and are of the same type. If yes, they form the Newton's third law pair.

Box on a Table: Clarifications

Weight example: Earth exerts gravity on the box (downward). The third-law pair is the box exerting gravity on the Earth (upward).
Normal-force example: The table exerts a normal force on the box (upward). The third-law pair is the box exerting a normal force on the table (downward).
The gravity and normal forces on the box are equal and opposite but are not Newton's third law pairs.

Quick Summary

For every force there is a Newton's third law pair; they are equal in magnitude, opposite in direction, and act on different objects. The pair is always of the same force type. Do not confuse weight/normal force within the same object as a third-law pair; identify the correct interacting objects (Earth and Box for gravity; Table and Box for normal force).