Rotational Motion and Angular Momentum - Physics (Undergraduate Foundation)

This course extends the principles of linear mechanics to rotational motion. It provides a complete analysis of the dynamics of rotating objects, covering the concepts of torque, angular momentum, and moment of inertia. Mastery of this material is essential for understanding any system that spins or orbits. The principles of rotational dynamics are fundamental to engineering and physics. They are required to analyse the operation of engines, turbines, and gyroscopes, and to model the orbital mechanics of planets and satellites. This course provides the required analytical tools for these complex systems. By the end of this course, you will be able to calculate torque for a given force, determine the moment of inertia for simple objects, apply the rotational equivalent of Newton's second law, and solve problems using the principle of conservation of angular momentum. This course is designed for first-year university students of physics and engineering. It is a mandatory course that builds directly on Newtonian dynamics and is a prerequisite for studying planetary mechanics and rigid body dynamics.

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Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
[NUC Core] PHY 101: General Physics I - Mechanics
[NUC Core] PHY 101: General Physics I - Mechanics
This learning track provides a complete and rigorous treatment of introductory classical mechanics as specified by the NUC Core Curriculum. It is structured to build a comprehensive analytical framework, starting with the mathematical description of motion (kinematics) and progressing through its causes (Newtonian dynamics), the powerful conservation laws, the dynamics of rotating systems, and finally, the principles of universal gravitation. Mastery of this material is the non-negotiable foundation for all subsequent study in physics and engineering. The principles of classical mechanics are the operational language for analysing the physical world. This track provides the essential toolset for solving problems in every field of engineering, from aerospace to civil, and for understanding phenomena from the trajectory of a projectile to the orbits of planets. By the end of this track, you will be able to analyse motion using vectors and calculus, apply Newton's laws to solve any standard dynamics problem, use conservation laws to analyse complex systems and collisions, analyse rotational motion, and solve problems in celestial mechanics. This learning track is a mandatory prerequisite for all first-year university students of physics, engineering, and related physical sciences. It provides the foundational knowledge required for all subsequent courses in mechanics, electromagnetism, thermodynamics, and modern physics.

This learning track provides a complete and rigorous treatment of introductory classical mechanics as specified by the NUC Core Curriculum. It is structured to build a comprehensive analytical framework, starting with the mathematical description of motion (kinematics) and progressing through its causes (Newtonian dynamics), the powerful conservation laws, the dynamics of rotating systems, and finally, the principles of universal gravitation. Mastery of this material is the non-negotiable foundation for all subsequent study in physics and engineering. The principles of classical mechanics are the operational language for analysing the physical world. This track provides the essential toolset for solving problems in every field of engineering, from aerospace to civil, and for understanding phenomena from the trajectory of a projectile to the orbits of planets. By the end of this track, you will be able to analyse motion using vectors and calculus, apply Newton's laws to solve any standard dynamics problem, use conservation laws to analyse complex systems and collisions, analyse rotational motion, and solve problems in celestial mechanics. This learning track is a mandatory prerequisite for all first-year university students of physics, engineering, and related physical sciences. It provides the foundational knowledge required for all subsequent courses in mechanics, electromagnetism, thermodynamics, and modern physics.

Course Chapters

1. Introduction
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This chapter introduces the dynamics of rotational motion. It establishes the fundamental quantities used to describe rotation and provides a direct comparison to their linear counterparts, setting the stage for analysing spinning and orbiting systems. Key objectives include understanding the course structure and the core concepts of rotational kinematics, torque, and angular momentum.

Chapter lessons

1-1. Welcome

A direct statement of the course's purpose and structure. This lesson outlines the progression from rotational kinematics to the principles of torque and angular momentum.

2. Fundamentals of Rotational Motion
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This chapter covers the kinematics of rotation. It defines the angular quantities used to describe how objects spin and establishes the equations for motion with constant angular acceleration, paralleling the concepts of linear motion. Key topics include angular displacement, velocity, and acceleration, the rotational kinematic equations, and the relationship between linear and angular variables.

Chapter lessons

2-1. Angular displacement, velocity, and acceleration

Defines the fundamental kinematic quantities for rotation. It establishes the conventions for direction and the standard units (radians) used in all rotational analysis.

2-2. Rotational kinematics

Introduces the set of equations for motion with constant angular acceleration. These are the direct rotational analogues of the linear kinematic equations.

2-3. Relating linear and angular variables

Covers the essential relationships between linear and angular quantities, such as v = rω. This allows for the analysis of the motion of points on a rotating object.

3. Rotational Dynamics and Torque
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This chapter introduces the cause of angular acceleration: torque. It defines torque, introduces moment of inertia as rotational mass, and establishes the rotational equivalent of Newton's second law, τ = Iα. Key topics include the definition of torque, the concept and calculation of moment of inertia for simple objects, and the application of the rotational second law to solve dynamics problems.

Chapter lessons

3-1. Defining torque

Formally defines torque as the rotational equivalent of force. It establishes the formula τ = rFsinθ and the right-hand rule for determining its direction.

3-2. Moment of inertia

Introduces the moment of inertia as a measure of an object's resistance to angular acceleration. It provides the general definition and formulas for common shapes.

3-3. Rotational second law

States the rotational analogue of Newton's Second Law: the net torque on an object is equal to its moment of inertia times its angular acceleration (Στ = Iα).

4. Angular Momentum
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This chapter introduces angular momentum and the law of its conservation. This is a fundamental conservation law in physics, critical for analysing systems without external torques, from spinning ice skaters to orbiting planets. Key topics include the definition of angular momentum for a particle and a rigid body, and the application of the law of conservation of angular momentum.

Chapter lessons

4-1. Defining angular momentum

Formally defines angular momentum for a rigid body as the product of its moment of inertia and angular velocity (L = Iω). It establishes angular momentum as a vector quantity.

4-2. Conservation of angular momentum

States the law of conservation of angular momentum: if the net external torque on a system is zero, its total angular momentum remains constant.

5. Conclusion
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This chapter consolidates the principles of rotational motion. It provides a structured summary of rotational kinematics, torque, moment of inertia, and angular momentum, reinforcing the core concepts of rotational dynamics. The conclusion summarises the key definitions and equations of rotational motion. It also provides a forward look to the final course on universal gravitation, where these principles are applied to orbital mechanics.

Chapter lessons

5-1. Summary of rotational mechanics

A concise review of the key concepts and equations of rotational motion. This lesson ensures the parallels between linear and rotational dynamics are consolidated.

5-2. Preparing for universal gravitation

Explains how the principles of rotational dynamics are a direct prerequisite for understanding the orbital mechanics of planets and satellites.