Newton's Law of Universal Gravitation

Описание: This lesson explains Newton's law of universal gravitation and how this inverse square law can be used to calculate gravitational force between two masses
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It also explains how the gravitational force prevents us from floating off the ground. In this lesson, we break down the inverse square law between two masses in a simple, intuitive way with real-world examples and full vector analysis.

What You’ll Learn

1. Understand and apply Newton’s law of universal gravitation
2. Use the gravitational formula to calculate force between any two masses
3. Interpret the vector form of gravitational force using unit vector r̂
4. Recognize how gravitational force is always attractive and universal
5. Explore how Newton’s third law applies to gravity with examples like the Earth-apple interaction
6. Calculate how mass and distance affect gravitational acceleration and force magnitudes

🔑 Key Concepts Covered

Newton's law of universal gravitation
gravitational force
gravitational constant (G)
inverse square law
Newton's third law
unit vector r̂
vector form of gravitational force
gravitational acceleration

Why This Lesson Matters

Understanding gravitational force is essential not just for AP and IB Physics exams but also for grasping how planets orbit, how tides work, and even how GPS satellites stay in space. Mastering this topic builds the foundation for deeper topics like orbital motion, gravitational potential energy, and Kepler’s laws.

🔗 Prerequisite or Follow-Up Lessons

(a) Watch “Newton’s First Law: The Law of Inertia” for foundational understanding of force
(b) Follow up with “Kepler’s Laws and Planetary Motion” to see how gravity governs orbital paths

📖 Full Lesson Transcript – Newton’s Law of Universal Gravitation

Gravity That’s “Just Right”
Have you ever thought that the force of gravity on Earth is just strong enough to keep us grounded—but not so strong that we’re crawling? And if gravity were any weaker, we might float away.

Isaac Newton realized that the same force pulling apples to the ground also keeps the Moon in orbit. The Moon’s forward velocity prevents it from falling straight down, resulting in an orbit.

Newton’s Big Idea: Universal Gravity
Newton proposed that every object in the universe attracts every other object with a force called gravitational force.

Take an apple with a mass of 0.1 kg. Using Earth’s gravity, it experiences a force: F = m × g = 0.1 × 9.8 ≈ 0.98 N

But here’s the key: Earth experiences the same force from the apple. Yet, since the Earth’s mass is enormous, its acceleration is nearly zero:

a = F/m = 0.98 / (5.972 × 10²⁴) ≈ 1.64 × 10⁻²⁵ m/s²

Newton’s Law of Gravitation – The Formula
Now, let’s understand the general law:

F = G × (m₁m₂ / r²)

Making It a Vector: Adding Direction with Unit Vectors
Force is a vector quantity. To include direction:

F = G × (m₁m₂ / r²) × r̂

Where r̂ is a unit vector pointing from one mass to the other. Important note:
r̂ gives direction only, not magnitude. It has no units. Don’t confuse r̂ with r, the scalar distance between masses

Newton’s Third Law and Opposing Forces
If F₁₂ is the force on mass 1 due to mass 2, then
F₂₁ = –F₁₂
That’s Newton’s third law in action. Both objects feel the same force in opposite directions. Gravity is always mutual and attractive.

Recap: Apple Pulls Earth Too!
Let’s compute the force Earth exerts on the apple (and vice versa):

F = (6.674 × 10⁻¹¹) × (0.1 × 5.97 × 10²⁴) / (6.371 × 10⁶)² ≈ 0.982 N
Then find Earth’s acceleration toward the apple:
a = F / m = 0.98 / (5.972 × 10²⁴) ≈ 1.64 × 10⁻²⁵ m/s²

That acceleration is so tiny that even in 13.8 billion years, Earth’s velocity would barely change by a fraction of a millimeter per second.

Who is this for: Class 11 physics student, AP Physics students, students appearing for competitive exams like IIT JEE and NEET. If you are looking for Class 11 physics notes or PDF downloads on the topic of Newton's laws of gravitation, gravitational potential energy etc., you should visit our website. You can find quiz and pdf summary of the topic.

Key Moments -
0:00 – Introduction: Why Doesn’t the Moon Crash Into Earth?
1:36 – Real-World Examples: Gravitational Force Between Everyday Objects
2:14 – Newton’s Law of Universal Gravitation Explained
3:36 – Vector Form of Gravitational Force and Unit Vector r̂
6:44 – Newton’s Third Law and Earth’s Acceleration Due to an Apple

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