Dynamics: Newton’s Laws of Motion – Study Notes

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Chapter 4: Dynamics – Newton’s Laws of Motion

4.1 Force

Force is a fundamental concept in physics, describing the interaction that causes a change in an object’s motion. Forces can alter the velocity of an object, affecting either its magnitude (speed), direction, or both.

Definition: A force is an external action that changes the velocity of a body.
Vector Nature: Force is a vector quantity, meaning it has both magnitude and direction.
Types of Forces: Forces are classified as contact forces (e.g., friction, tension, normal) or long-range forces (e.g., gravity).
Net Force: The combined effect of all forces acting on an object is the net force:

Measurement: The magnitude of a force can be measured using a spring scale.

Weight

The gravitational pull of the Earth on an object near its surface.
Symbol: w (also Fw or Fg).
Always points vertically downward.
Weight is not the same as mass.
It is the only force in this course that does not require contact between objects.

, where

Mass and Weight Comparison

Mass: Property of an object, measures the amount of matter (unit: kg).
Weight: Force, measures the strength of gravitational interaction (unit: Newton).

	Earth	Moon
Mass	m	m
Weight

Tension Force

A contact force (a pull) exerted by a rope or string.
Symbol: T (sometimes FT).
Direction: Always along the string or rope.

Normal Force

A contact force (a push) exerted by a surface against an object pressing on it.
Symbol: N (sometimes FN).
Direction: Always perpendicular to the surface.

Spring Force (Hooke’s Law)

A contact force exerted by a spring, which can push (compressed) or pull (stretched).
Symbol: Fsp
Any elastic material can act as a spring.

k: Spring constant
x: Displacement from equilibrium position ()
The negative sign indicates a restoring force (acts to return to equilibrium).

4.2 Newton’s First Law of Motion (Law of Inertia)

Newton’s First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force.

Law of Inertia: Resistance of an object to changes in its state of motion.
Friction is a force that opposes motion and can bring moving objects to rest.

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

Example: When a school bus stops suddenly, backpacks slide forward due to inertia.

Inertial Reference Frames

Newton’s First Law holds only in inertial reference frames (not accelerating or rotating).
Non-inertial frames (accelerating/rotating) require fictitious forces for Newton’s laws to apply.

4.3 Mass

Mass is a measure of an object’s inertia and is a fundamental property of matter.

Measured in kilograms (kg) in the SI system.
Mass is constant regardless of location (e.g., Earth or Moon).
Weight depends on the local gravitational field; mass does not.

4.4 Newton’s Second Law of Motion

Newton’s Second Law quantifies the relationship between force, mass, and acceleration.

Formula:

Force and acceleration are vectors; the law applies to each coordinate axis.
The SI unit of force is the newton (N):

More force produces more acceleration; more mass results in less acceleration for the same force.

System	Mass	Force
SI	kilogram (kg)	newton (N)
cgs	gram (g)	dyne (g·cm/s²)
British	slug	pound (lb)

Example: Calculating the force required to stop a car of mass 1500 kg from 100 km/h to rest over 55 m.

4.5 Newton’s Third Law of Motion

Newton’s Third Law describes the mutual interactions between objects.

Statement: Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.
Forces always occur in pairs, acting on different objects.
Notation: is the force on A due to B; .
Example: Rocket propulsion – the rocket expels gases backward, and the reaction force propels the rocket forward.

Important: Action-reaction pairs do not cancel because they act on different objects.

4.6 Weight—the Force of Gravity; and the Normal Force

When an object rests on a surface, the force of gravity is balanced by the normal force exerted by the surface.

Normal Force: Acts perpendicular to the surface, balancing the weight of the object.
If the normal force exceeds the strength of the surface, the surface may break.

Example: Calculating the normal force on a box at rest and when an additional downward force is applied.
Example: Apparent weight loss in an accelerating elevator (scale reading changes with acceleration).

4.7 Solving Problems with Newton’s Laws: Free-Body Diagrams

Free-body diagrams are essential tools for analyzing forces acting on objects.

Draw a sketch of the situation.
Draw a free-body diagram for each object, showing all forces with correct magnitudes and directions. Label each force.
Resolve vectors into components (usually x and y axes).
Apply Newton’s Second Law to each component.
Solve the resulting equations for the unknowns.

Example: Analyzing the forces on a hockey puck sliding on frictionless ice.
Example: Two boxes connected by a cord, finding acceleration and tension.
Example: Using a pendulum as an accelerometer in a car to measure acceleration.

4.8 Problem Solving – A General Approach

Effective problem solving in dynamics involves a systematic approach:

Read the problem carefully, more than once.
Draw a sketch and a free-body diagram.
Choose a convenient coordinate system.
List known and unknown quantities; relate them with equations.
Estimate the answer.
Solve algebraically before substituting numbers.
Check units and dimensions.
Assess if the answer is reasonable.

Summary Table: Newton’s Laws and Related Concepts

Law/Concept	Statement/Formula
Newton’s First Law	If net force is zero, object remains at rest or in uniform motion.
Newton’s Second Law
Newton’s Third Law
Weight
Hooke’s Law (Spring)

Additional info: These notes include expanded explanations, examples, and tables for clarity and exam preparation.