Unit 2: Force and Translational Dynamics

Introduction

Gravity is a fundamental force that attracts two masses toward each other. Newton’s Law of Universal Gravitation describes the gravitational force between two objects, while weight is the force due to Earth's gravity.

Formula for Gravitational Force:

F = G (m₁m₂) / r²

• F = gravitational force (N)
• G = gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
• m₁, m₂ = masses of the objects (kg)
• r = distance between the centers of the masses (m)

Key Concepts

• Gravity is always attractive—it pulls objects together.
• The gravitational force decreases as the distance between objects increases.
• Weight (W) is the force of gravity acting on an object near Earth: W = mg
• Acceleration due to gravity (g): 9.8 m/s² near Earth's surface.
• All objects experience the same acceleration in free fall, regardless of mass (ignoring air resistance).

Applications of Gravitational Force

• Planetary Motion: Gravity keeps planets in orbit around the Sun.
• Free Fall: Objects accelerate downward at 9.8 m/s² when dropped.
• Satellites: Orbiting objects experience gravitational attraction but remain in motion due to their velocity.

Mathematical Routines

Use these equations to solve gravitational force problems:

• Universal Gravitation: \( F = G \frac{m_1 m_2}{r^2} \)
• Weight: \( W = mg \)
• Gravitational acceleration: \( g = \frac{GM}{r^2} \), where \( M \) is a planet's mass.

Practice Activities

Summary & Exam Preparation Tips

Gravitational force is essential for understanding motion on Earth and in space. Key takeaways:

• Gravitational force follows an inverse-square law (\( F \propto 1/r^2 \)).
• Weight is different from mass—weight depends on gravity.
• Objects in orbit are in free fall, constantly falling toward the planet while moving sideways.

Practicing force calculations and understanding gravitational relationships will prepare you for AP Physics problems.