---
title: Physics — Classical Mechanics
lang: en
description: Foundational equations of Newtonian mechanics. Demonstrates the `formula`, `name-formula`, and `pitfall` card types.
tags:
  - physics
  - mechanics
  - formulas
  - latex
visibility: private
---

# Physics — Classical Mechanics

> Front shows a LaTeX equation; back is a Markdown explanation with variable definitions.
> Demonstrates the **formula**, **name-formula**, and **pitfall** card types.

---

## Front

F = ma

## Back

**Newton's second law of motion.**

- $F$ — net force on a body (N)
- $m$ — mass of the body (kg)
- $a$ — acceleration produced (m/s²)

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

<!-- card:
  cardType: formula
  subject: Physics
  topic: Newton's laws
  prompt: "Recall the formula and what each variable means."
  difficulty: easy
-->

---

## Front

p = mv

## Back

**Linear momentum.**

- $p$ — momentum (kg·m/s)
- $m$ — mass (kg)
- $v$ — velocity (m/s, vector)

Momentum is conserved in any closed system with no external forces.

<!-- card:
  cardType: formula
  subject: Physics
  topic: Momentum
  prompt: "What does this equation describe?"
  difficulty: easy
-->

---

## Front

E_k = \tfrac{1}{2} m v^{2}

## Back

**Kinetic energy.**

- $E_k$ — kinetic energy (J)
- $m$ — mass (kg)
- $v$ — speed (m/s)

Doubling speed **quadruples** the kinetic energy.

<!-- card:
  cardType: formula
  subject: Physics
  topic: Energy
  prompt: "Why is the speed squared?"
  difficulty: medium
-->

---

## Front

F = G \dfrac{m_{1} m_{2}}{r^{2}}

## Back

**Newton's law of universal gravitation.**

- $G$ — gravitational constant ($6.674 \times 10^{-11}$ N·m²/kg²)
- $m_1, m_2$ — the two masses (kg)
- $r$ — distance between their centers (m)

Inverse-square law: doubling the distance reduces the force by a factor of 4.

<!-- card:
  cardType: formula
  subject: Physics
  topic: Gravitation
  difficulty: medium
-->

---

## Front

Hooke's Law

## Back

F = -kx

- $F$ — restoring force (N)
- $k$ — spring constant (N/m)
- $x$ — displacement from equilibrium (m)

The negative sign indicates the force is opposite to the displacement.

<!-- card:
  cardType: name-formula
  subject: Physics
  topic: Oscillations
  direction: name->formula
  backType: latex
  prompt: "Write the equation and define each term."
  difficulty: easy
-->

---

## Front

T = 2\pi \sqrt{\dfrac{L}{g}}

## Back

**Period of a simple pendulum.**

- $T$ — period of one full oscillation (s)
- $L$ — length of the pendulum (m)
- $g$ — gravitational acceleration (m/s²)

Independent of mass and (for small angles) independent of amplitude.

<!-- card:
  cardType: name-formula
  subject: Physics
  topic: Oscillations
  direction: formula->name
  difficulty: medium
-->

---

## Front

> Common mistake: confusing **mass** and **weight**.

## Back

**Mass** ($m$, kg) is an intrinsic property — how much matter a body contains.

**Weight** ($W$, N) is the gravitational force on that mass: $W = mg$.

A 1 kg block has the same mass on the Moon as on Earth, but only ≈ 1/6 the weight.

✅ **Better alternative:** When asked for "weight in kilograms" in everyday speech, the answer is mass; only convert to newtons when forces are required.

<!-- card:
  cardType: pitfall
  subject: Physics
  topic: Units
  frontType: markdown
  backType: markdown
  prompt: "Spot the mistake before flipping."
  difficulty: easy
-->