# Newton's Laws of Motion

Physics I · Principles of Mechanics · https://tryals.app/learn/physics-i/newtons-laws-of-motion

## The Laws of Motion

Steady motion needs no force at all; forces only explain **changes** in motion. The second law runs both ways: ask what net force acts to find acceleration, or see acceleration to know the net force.

**Newton's three laws** form classical mechanics:

| Law | Core Rule | Statement |
| --- | --- | --- |
| **First (Inertia)** | Zero Net Force | A body stays at rest or in uniform motion unless acted on by a net external force. |
| **Second** | $\vec{F}_{\text{net}} = m\vec{a}$ | Only the **vector sum** of all forces determines acceleration. |
| **Third** | Action-Reaction | If body A exerts a force on body B, B exerts an equal and opposite force on A. |

**Common pitfall**: Action-reaction pairs **never cancel** because they act on **different** bodies. The book's weight and the table's normal force on it are NOT a third-law pair; both act on the book itself.

## Free-Body Diagrams & Forces

**Free-body diagrams** are the essential tool for applying Newton's laws: isolate the object, draw all forces acting **on** it, choose coordinate axes, and apply $\sum F_x = ma_x$ and $\sum F_y = ma_y$.

**Common forces** quantify these interactions:

| Force | Formula | Direction | Meaning |
| --- | --- | --- | --- |
| **Weight** | $W = mg$ | Downward | Gravitational pull ($m$ is mass, $g$ is gravity). |
| **Normal** | $N$ | Perpendicular | Support force from a surface. |
| **Kinetic friction** | $f_k = \mu_k N$ | Opposing motion | Friction during sliding ($\mu_k$ is kinetic coefficient). |
| **Static friction** | $f_s \leq \mu_s N$ | Opposing tendency | Friction before sliding starts ($\mu_s$ is static coefficient). |
| **Tension** | $T$ | Along string | Pulling force exerted by a taut rope or string. |

## Practice questions

6 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. Order the steps for solving a Newton's second law problem.

**Answer:**

1. Draw a free-body diagram
2. Choose a coordinate system
3. Write $\Sigma F = ma$ for each axis
4. Substitute known values
5. Solve for the unknown

**Why:** This systematic approach prevents sign and direction errors.

Page: https://tryals.app/practice/physics-i/newtons-laws-of-motion/order-the-steps-for-solving-a-newtons-second-law-problem

### 2. A horse pulls a cart. By Newton’s third law the cart pulls back on the horse **just as hard**. How can the pair ever accelerate?

A. They cannot accelerate unless friction is zero
B. The third law stops applying once motion starts
C. The two forces act on different bodies
D. The horse pulls slightly harder than the cart pulls back

**Answer:** C. The two forces act on different bodies

**Why:** Each body accelerates according to the net force on **it alone**. The cart feels the horse’s pull (forward) minus friction; the horse feels the cart’s pull (backward) plus the ground pushing it forward. Both nets can be forward at once.

Page: https://tryals.app/practice/physics-i/newtons-laws-of-motion/a-horse-pulls-a-cart-by-newtons-third-law-the-cart-pulls-back-on

### 3. A book rests on a table. Sort each force pairing: is it a genuine **Newton’s third-law pair**?

**Answer:**

- Third-law pair: Earth pulls book down / book pulls Earth up, Table pushes book up / book pushes table down
- Not a third-law pair: Earth pulls book down / table pushes book up, Book’s weight / book’s normal force

**Why:** Third-law partners swap the roles of the two objects: "A on B" pairs with "B on A", same kind of force. Weight (Earth on book) and normal force (table on book) merely happen to balance while the book is in equilibrium.

Page: https://tryals.app/practice/physics-i/newtons-laws-of-motion/a-book-rests-on-a-table-sort-each-force-pairing-is-it-a-genuine

### 4. Newton's first law states that an object at rest will remain at rest unless acted upon by a net external force.

**Answer:** True

**Why:** This is the law of inertia: no net force $\to$ no change in motion.

Page: https://tryals.app/practice/physics-i/newtons-laws-of-motion/newtons-first-law-states-that-an-object-at-rest-will-remain-at-rest

### 5. Match each of Newton's laws to its key concept.

**Answer:**

- First law → Inertia
- Second law → $F = ma$
- Third law → Action-reaction pairs
- Universal gravitation → $F = Gm_{1}m_{2}/r^{2}$

**Why:** Newton formulated three laws of motion and the law of gravitation.

Page: https://tryals.app/practice/physics-i/newtons-laws-of-motion/match-each-of-newtons-laws-to-its-key-concept

### 6. Which forces act on a book resting on a table? (Select all that apply)

A. Applied force forward
B. Friction force to the right
C. Gravity (weight) downward
D. Normal force upward

**Answer:** C. Gravity (weight) downward; D. Normal force upward

**Why:** A stationary book on a table has only weight and normal force.

Page: https://tryals.app/practice/physics-i/newtons-laws-of-motion/which-forces-act-on-a-book-resting-on-a-table-select-all-that-apply