Dynamics: Forces and Newton's Laws of Motion

Newton's First Law

An object at rest remains at rest, and an object in motion remains in motion at a constant velocity, unless acted upon by a net external force.

Inertia

The property of matter to resist changes in its motion.

Inertial Reference Frames

Frames that are not accelerating.

Equilibrium

A state where the sum of all forces acting on a system is zero.

Static Equilibrium

A condition where an object is at rest (v = 0, a = 0).

Dynamic Equilibrium

A condition where an object is moving at a constant velocity (v ≠ 0, a = 0).

Newton's Second Law

States that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Net Force Equation

 962F = m6F; describes the relationship between net force, mass, and acceleration.

Component Analysis

Breaking down forces and accelerations into their respective axes for better understanding.

Newton's Third Law

States that for every action, there is an equal and opposite reaction.

Action and Reaction Forces

Forces that occur simultaneously but act on different objects.

Free Body Diagram (FBD)

A diagram used to isolate an object of interest, representing all forces acting on it.

Gravitational Force (Weight)

The force strictly due to gravity, calculated as W = mg.

Normal Force

A reactive contact force exerted by a surface, perpendicular to that surface.

Tension

A pulling force transmitted through a string, rope, or cable.

Friction

A resistive force that opposes motion or potential motion.

Static Friction

A variable force that prevents slipping, matching applied force up to a maximum limit.

Kinetic Friction

A constant force that acts when there is relative sliding between surfaces.

Spring Force (Hooke's Law)

The restoring force exerted by an ideal spring, given by F_s = -k*x.

Drag Force

The force exerted by air resistance, which depends on velocity.

Terminal Velocity

The constant velocity achieved when the drag force equals the weight of an object.

Inclined Plane

A flat surface tilted at an angle, used to reduce the force needed to lift objects.

Atwood Machine

A system of two masses connected by a string over a pulley, used to analyze forces.

Centripetal Force

The net force that causes an object to move in a circular path.

Uniform Circular Motion

Motion in a circle at a constant speed.

Non-Uniform Circular Motion

Motion in a circle where speed changes; it has both radial and tangential acceleration.

Banked Curves

Curves designed to allow vehicles to turn at a speed without relying solely on friction.

Fictitious Force Fallacy

The misconception of an outward force felt during a turn, which is actually due to inertia.

Normal Force Assumption

The incorrect assumption that Normal Force is automatically equal to weight under all circumstances.

Static Friction Misunderstanding

Confusing the maximum static friction with actual static friction, which only matches the applied force.

Third Law Confusion

The misunderstanding that action-reaction forces must act on the same object.

Mathematic Condition for Equilibrium

 962F = 0, indicates the sum of forces in all directions equals zero.

Dragging Force (F_D)

A force opposing motion, varying with speed and environment.

Acceleration Equation for Circular Motion

ma_c = mv^2/r; describes the relationship between force and circular motion.

Velocity as a Function of Time

The relationship derived from integrating the forces acting on an object.

Deceleration Effect

When an object in motion feels an inertial effect when a reference frame decelerates.

Force Interaction

Describes how forces act equally and oppositely on different objects.

Spring Constant (k)

A measure of a spring's stiffness, expressed in N/m.

Kinematic Variables

Quantities describing motion, such as position, velocity, and acceleration.

Force Vector

A representation of force that has both magnitude and direction.

Equilibrium in Multiple Dimensions

A state where forces in all dimensions equal zero for a static system.

System Approach for Dynamics

Analyzing the entire system to find the net acceleration and net forces involved.

Individual FBD Analysis

Drawing Free Body Diagrams for each object to solve for forces separately.

Mass Density Relationship

The correlation of mass to volume in objects, impacting force analysis.

Energy Conservation Principle

The principle that states energy in a closed system remains constant.

Momentum Conservation

The principle dictating that total momentum in an isolated system remains constant.

Force Components in Dynamics

Breaking forces into x and y components for detailed analysis.