Lecture: Understanding Gyroscopes

Overview

A gyroscope is a device that can either:
- Provide information about the variation of orientation of a system with respect to a reference axis.
- Provide information about the angular velocity of a rotating system.
Used widely in:
- Phones
- Aeronautics
- Video game consoles
- Robotics
The human vestibular system acts as a natural gyroscope.

Key Concepts:
- Torque: Generated when force is applied away from axis of rotation.
- Angular Momentum: Depends on moment of inertia and angular velocity.
Newton's Laws:
- If net external torque is zero, angular momentum remains constant.
- Torque = rate of change of angular momentum.
Applications:
- Spatial Rigidity: A rotating disk maintains orientation if no external torque acts.
  - Example: Foucault's gyroscope.
- Precession: Circular motion created when a rotating object is subjected to a force.
  - Used to determine system speed.
Limitations:
- Large size and mass required for accuracy.

Coriolis Acceleration: Occurs when a particle moves radially during rotation.
Principle:
- The force on oscillating mass allows calculation of angular velocity.
Applications:
- Ideal for small-sized tech (e.g., smartphones).
Limitations:
- Susceptible to errors from large linear accelerations.

Sagnac Effect: Difference in light beam path lengths due to system rotation.
Principle:
- Use of two light beams in opposite directions to measure phase shift and thus angular velocity.
Advantages:
- High accuracy and reliability.
- No moving parts.
- Miniaturization possible (e.g., 2mm square gyroscope at Caltech).