Patterns of Motion and Equilibrium: Key Concepts

In the absence of force, objects in motion tend to continue moving indefinitely.
No force is necessary to keep a horizontally moving object moving when there's no friction.
Inertia is the property of objects to resist any change in their state of motion.

Mass: amount of matter composing an object.
Greater mass \Rightarrow greater inertia; smaller mass \Rightarrow smaller inertia.
Mass is a measure of an object's resistance to changes in its state of motion.
Standard unit for mass: kilogram ( \text{kg} ).
1 \text{ kg} of material weighs approximately 9.8 \text{ Newtons} on Earth.

Density is the measure of how much mass occupies a given space (compactness).
Equation: \text{Density} = \frac{\text{mass}}{\text{volume}} .
Units: \text{g/cm}^3 or \text{kg/m}^3 .
The density of an object (e.g., 1 \text{ kg} of iron) is the same regardless of location (e.g., Earth vs. Moon) because both mass and volume remain constant.

For a non-accelerating object or system, the vector sum of forces acting on it equals zero.
Mathematical notation: \Sigma F = 0 .
This rule applies to vector quantities.
An object with a net force of zero is in mechanical equilibrium.

The force that supports an object on the surface of another object against gravity.
In equilibrium (e.g., a book on a table), the support force balances the object's weight.

An object moving at constant velocity is in dynamic equilibrium.
This also implies that the two or more forces acting on it cancel to zero (i.e., \Sigma F = 0 ).
An object at rest or moving with constant velocity is in equilibrium.

A resistive force that opposes the motion (or attempted motion) of an object over a surface or through a fluid.
Acts in a direction opposing motion.
Amount depends on the materials in contact and how much they are pressed together.
Friction can occur with sliding objects, in water, and in air.
When an object moves at constant speed, the force of friction is equal and opposite to the applied push.

Speed: distance covered per amount of travel time.
- \text{Speed} = \frac{\text{distance covered}}{\text{travel time}} .
- Average speed: \frac{\text{total distance covered}}{\text{travel time}} .
- Instantaneous speed: speed at any given instant.
- Speed is a scalar quantity (magnitude only).
Velocity: speed and direction of an object.
- Velocity is a vector quantity (magnitude and direction).
Motion is relative; speeds are usually considered relative to the Earth's surface.

Acceleration is the rate at which velocity changes with time.
It can involve a change in magnitude, direction, or both.
Equation: \text{Acceleration} = \frac{\text{change of velocity}}{\text{time interval}} .
Units: (e.g., \text{m/s}^2 ).
An automobile cannot maintain constant velocity when accelerating or rounding a curve (as direction changes).

Occurs when gravity is the only force acting on a falling object (negligible air resistance).
In free fall, an object's velocity increases constantly with time.
On Earth, the acceleration due to gravity is approximately 10 \text{ m/s}^2 .
During free fall, speed increases by 10 \text{ m/s} each second.
The distance fallen by a free-falling body increases each second, proportional to time squared.
Equation for distance of free fall from rest: \text{D} = \frac{1}{2}\text{gt}^2 .