Foundations of Dynamics: Unit 2 Study Guide

Newton's First Law

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

Inertia

The inherent property of matter that describes an object's resistance to changes in its state of motion.

Equilibrium

A state where the net force acting on an object is zero, resulting in no acceleration and constant velocity.

Static Equilibrium

The condition of an object at rest with zero acceleration and velocity.

Dynamic Equilibrium

The condition of an object moving at a constant velocity with zero acceleration.

Inertial Reference Frame

A frame of reference where Newton's laws are valid and which is not accelerating.

Free-Body Diagram (FBD)

A graphical representation that shows all the external forces acting on an object.

Isolate the Object (FBD Rule)

Draw the object as a simple dot or a box, ignoring surroundings.

External Forces Only (FBD Rule)

Include only forces acting on the object, not forces the object exerts on others.

Vector Origin (FBD Rule)

All force vectors must originate from the center of the object and point away from it.

The Fundamental Equation of Newton's Second Law

The net force acting on an object equals the mass of the object multiplied by its acceleration: (  \sum \vec{F} = m\vec{a} ).

Newton's Second Law (calculus-based)

The net force acting on an object is the time derivative of momentum: ( \sum \vec{F} = \frac{d\vec{p}}{dt} ) with ( \vec{p} = m\vec{v} ).

Component Analysis

Breaking down forces and accelerations into their perpendicular components for analysis.

Crucial Exam Rule for FBDs

Never draw vector components on the main FBD; do so on a separate scratch work diagram.

Newton's Third Law

For every action, there is an equal and opposite reaction: If Object A exerts a force on Object B, then Object B exerts an equal and opposite force on Object A.

Interaction Pairs (Third Law)

Forces that occur between two different objects and do not cancel each other on a single FBD.

Total Mass in F=ma

When summing forces in a system, the ( m ) in ( \sum F = ma ) must be the total mass of the system.

Normal Force (N)

The force perpendicular to the surface; it varies with incline and external forces and is not always equal to gravity.

Centripetal Force

Not a real force; it is the net force causing circular motion and is provided by other forces such as tension, gravity, or friction.

Common Mistake regarding Third Law Cancellation

Students often mistakenly believe Third Law pairs cancel out; they only cancel when considering the system as a whole.

Misunderstanding Inertia vs. Force

Objects do not carry a 'force of motion'; they continue in their state of motion unless acted upon by external forces.

Dynamic Equilibrium Indicators

Key terms indicating dynamic equilibrium include 'constant speed', 'terminal velocity', and 'no acceleration'.

FBD Labeling

Use standard notation for forces such as ( Fg ) for gravity and ( FN ) for normal force.

Acceleration in Terms of Net Force

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

Inclined Plane Acceleration Formula

For a block on an incline, ( ax = g(\sin\theta - \muk\cos\theta) ), where ( \mu_k ) is the coefficient of kinetic friction.

Drawing an FBD for an Inclined Plane

Analyze forces in both x and y directions separately when determining acceleration and forces on the ramp.

Example of Interaction Pairs

In the case of a horse pulling a cart, the horse feels the cart's pull backward while using friction from the ground to move forward.