🧲 Newton’s Laws

~ 📖 Definition ~

Force is a vector quantity that represents a push or pull exerted on an object. It causes an object to accelerate, decelerate, remain still, or change direction.

Forces are measured in Newtons (N).
N = 1 kg·m/s², meaning 1 N will accelerate a 1 kg mass by 1 m/s².

~ ⚖️ Newton's Laws of Motion ~

1. Inertia (First Law)

An object at rest stays at rest, and an object in motion continues at constant velocity (same speed and direction), unless acted upon by a net external force.
Objects with more mass have more inertia — meaning heavier objects require more force to start or stop moving.

2. Second Law of Motion

$$\vec{F}_{\text{net}} = m \vec{a}$$

The net force on an object equals its mass times acceleration.
For example, gravitational force can be calculated by measuring the acceleration of a falling object and its mass.
Rearranged:

$$\vec{a} = \frac{\vec{F}_{\text{net}}}{m}$$

3. Third Law of Motion

For every action, there is an equal and opposite reaction.
For example, when an object rests on a surface, the surface exerts an upward Normal force equal and opposite to the gravitational force, resulting in zero net force.

——— 🛑 Friction: Static and Kinetic ———

~ 📚 Definition ~

Static friction: Force that resists the start of motion between two surfaces in contact. Acts when the object is stationary.
Kinetic friction: Force opposing motion when two surfaces slide past each other. Acts when the object is moving.

~ 📏 Magnitude ~

Static friction adjusts up to a maximum:

$$F_{\text{static}} \leq \mu_s N$$

where $\mu_s$ is the coefficient of static friction, and $N$ is the normal force.

Kinetic friction has a constant magnitude once moving:

$$F_{\text{kinetic}} = \mu_k N$$

where $\mu_k < \mu_s$ typically.

~ 🔑 Key Points ~

Static friction must be overcome to start motion.
Kinetic friction acts continuously to resist motion once started.
Coefficients $\mu_s$ and $\mu_k$ depend on the materials in contact.
Both forces are proportional to the normal force; coefficients are dimensionless.

——— 🔄 Uniform Circular Motion ———

~ 🔄 Centripetal Force ~

$$F_c = \frac{m v^2}{r}$$

Where:

$F_c$ = centripetal force (Newtons)
$m$ = mass (kg)
$v$ = velocity (m/s)
$r$ = radius of circle (m)

Explanation

Force points toward center of circle.
Perpendicular to velocity.
Faster speed or smaller radius → stronger force required.
Velocity squared because acceleration $a = \frac{v^2}{r}$ and $F = m a$.
Doubling speed → quadruples required force.

Note

If centripetal force disappears, the object moves in a straight line tangent to the circle at release.

~ 🌀 Centrifugal Force ~

Not a real force — an apparent force felt in a rotating frame.
Example: on a merry-go-round, feeling pushed outward is centrifugal force.
Real force acting inward is centripetal force keeping you moving in a circle.

——— 🌌 Newtonian Gravity (Universal Law of Gravitation) ———

~ ❓ What is G? ~

$G$ is the gravitational constant, a fixed number used in the formula.
It tells us how strong gravity is in general.
Its value is:

$$G = 6.674 \times 10^{-11} \text{ N·m}^2/\text{kg}^2$$

——— 🧲 Newton’s Laws ———

——— ✊ Forces ———