## Newton's Laws of Motion

Based on the following assumptions:

• $mass = density \times volume$
• $momentum = mass \times velocity$
• $force = \text{an action on an object that changes its motion}$
• $\text{the motion of an object is uniform, if its velocity is constant}$

### First Law of Motion

Unless acted on by some force an object stays at rest or in uniform motion.

$force = \text{anything capable of changing the motion of an object}$

Equal forces cancel each other out (e.g. a tug-of-war stalemate, an object hanging from a support by a string).

### Second Law of Motion

The force on an object is proportional to the rate of change of momentum of the object.

$F = kma$

$k = 1$

• an object decelerates whena force acts on it in the opposite direction of its movement
• force of gravity is produced by an objects weight pushing it down

### Unit Force

$N$ (newtons)

### Mass and Weight

$W = mg$ where

$m = \text{mass in kilograms}$
$g = \text{acceleration of a freely falling object}$

Since $g = 9.8m/s^2$ near earth's surface, the weight of a mass $1kg$ on earth is $9.8N$.

Since weight is a force, its unit is newtons.

### Gravitational Field Strength

The force of gravity per unit mass on an object at that position.

$g = 9.8N/kg$ or
$g = 9.8m/s^2$

### Third Law of Motion

When two bodies interact, they exert equal and opposite forces on each other.

## Stability

### Vectors

A physical quantity with direction and size.

• Force
• Velocity
• Acceleration
• Momentum

Vectors in diagrams are depicted as arrows pointing in directions.

### Scalars

A physical quantity without direction.

• Distance
• Speed
• Mass

### Center of Gravity / Center of Mass

A concept that keeps objects in stable equilibrium when they stand straight upright.

For free standing objects, the lower the center of gravity the more stable the object stands.