4.2 Newton's Laws of Motion

Newton's laws of motion form the foundation of classical mechanics. These three principles explain how forces affect objects, from a book resting on a table to a rocket launching into space. Understanding these laws helps us predict and analyze motion in everyday situations.

Applying Newton's laws reveals the hidden forces shaping our world. From the inertia that keeps us in our seats during a car ride to the action-reaction pairs propelling a swimmer through water, these laws govern the physics of motion all around us.

Newton's Laws of Motion

Newton's three laws of motion

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• First Law (Law of Inertia)
  • Objects maintain state of motion or rest unless external force acts upon them
  • Inertia resists changes in motion, proportional to object's mass
  • Examples: passengers lean forward when bus stops suddenly, coin on paper flicked off table
• Second Law (Law of Force and Acceleration)
  • Net force equals mass times acceleration [F = ma](https://www.fiveableKeyTerm:f_=_ma)
  • Doubling force doubles acceleration, doubling mass halves acceleration
  • Examples: pushing shopping cart (light vs heavy), rocket thrust in space
• Third Law (Law of Action-Reaction)
  • Forces always occur in pairs, equal in magnitude and opposite in direction
  • Action and reaction forces act on different objects, don't cancel out
  • Examples: recoil of gun, fish propelling through water by pushing against it

Applications of Newton's first law

• Objects at rest
  • Remain stationary when forces balanced (net force zero)
  • Examples: book on table (gravity balanced by normal force), car at red light
• Objects in motion
  • Maintain straight-line motion at constant velocity without net force
  • Examples: spacecraft in deep space, air hockey puck on frictionless table
• Practical applications
  • Seat belts protect passengers by counteracting inertia during sudden stops
  • Objects slide farther on ice than rough pavement due to reduced friction
  • Tightrope walkers use long poles to adjust center of mass and maintain balance

Calculations with Newton's second law

• Rearrange $F = ma$ to find acceleration $a = F / m$
• Net force is vector sum of all forces acting on object
• Steps to calculate acceleration:
  1. Identify all forces acting on object (gravity, friction, applied forces, normal force)
  2. Determine net force by adding vector components
  3. Divide net force by object's mass
• Units: acceleration (m/s²), force (N), mass (kg)
• Example calculations:
  • Car accelerating: consider engine force, friction, air resistance
  • Object falling: account for gravitational force and air resistance
  • Block sliding down inclined plane: resolve forces into components

Force pairs in Newton's third law

• Characteristics of action-reaction pairs
  • Equal magnitude, opposite direction, act on different objects
  • Don't cancel out as they act on separate bodies
• Common examples
  • Person pushing wall: hands exert force on wall, wall pushes back on hands
  • Rocket propulsion: exhaust gases pushed backward, rocket propelled forward
  • Walking: feet push ground backward, ground pushes feet forward
• Analyzing force diagrams
  • Identify all forces on each object separately
  • Consider action-reaction pairs for interacting objects
  • Example: book on table (weight of book on table, normal force of table on book)
• Applications in sports
  • Swimming: arms push water backward, water propels swimmer forward
  • Jumping: legs push down on ground, ground pushes up on person