Introduction

Rotational dynamics deals with the motion of rotating bodies and the forces causing such motion. It extends the concepts of linear motion to rotational motion, involving angular displacement, velocity, and acceleration.

Step-by-Step Explanation of Rotational Dynamics

1. Moment of Inertia (I)

The moment of inertia measures an object's resistance to change in its rotational motion. For a point mass m at a distance r from the axis:

For extended bodies, the total moment of inertia is the sum of all point masses:

2. Torque (τ)

Torque is the rotational equivalent of force, causing angular acceleration. Defined as:

where r is the lever arm and F is the force applied at an angle θ.

3. Newton's Second Law for Rotation

The angular equivalent of Newton's second law:

where α is the angular acceleration.

4. Kinetic Energy of Rotation

Rotational kinetic energy:

where ω is the angular velocity.

5. Work and Power

Work done by torque:

Power:

6. Conservation of Angular Momentum

Angular momentum L:

If no external torque acts, L remains constant.

Assessment Methods

• Periodic Quizzes
• Mid-term Exams
• Laboratory Experiments on Rotational Motion
• Final Examination
• Project and Assignments