Rotational Motion Lecture Notes

Introduction

• Covered basics of translational motion so far.
• Now introducing rotational motion.
• Rotational motion affects real-life examples like a football's spin.

Key Concepts in Rotational Motion

• Involves position, velocity, and acceleration like translational motion.
• Uses different terms: angles instead of positions, arcs instead of lines.

Key Differences

Instead of positions: angles (theta).

• Instead of lines: arcs.
• Example: A point on a spinning wheel can be standing still.

Describing Position in Rotational Motion

• Translational motion uses x and y axes.
• Rotational motion focuses on angle (theta).
• Measured from the top of a circle:
  • 0 degrees at the top
  • 180 degrees at the side

Radians

• Physicists often use radians over degrees.
• Radian based on circle's radius.
  • 360 degrees = 2π radians.
  • 180 degrees = π radians.
• Conversion: degrees × (π / 180).

Velocity in Rotational Motion

• Linear velocity: change in position.
• Angular velocity: change in angle (Omega, ω).
  • Derivative of angular displacement over time.

Tangential Velocity

• Discussed in uniform circular motion.
• Perpendicular to the radius in the direction of motion.
• Tangential velocity = angular velocity × radius.

Periodic Rotational Motion

• Periodic: rotation repeats after a set time (T, The Period).
• Frequency: number of rotations per second.
• Conversion: frequency × 2π = angular velocity.

Rolling Without Slipping

• Common in real-life (car tires, train wheels).
• At the bottom of the wheel: translational velocity = 0 (no slipping).
• Total velocity at the bottom is zero: translational velocity – tangential velocity =0.

Angular Acceleration

• Angular acceleration: derivative of angular velocity (Alpha, α).
• Components:
  • Radial (centripetal) acceleration: inward, angular velocity² × radius.
  • Tangential acceleration: affects how fast points are speeding up/slowing down, angular acceleration × radius.

Summary

• Similarities between linear and angular motion equations.
• Covered angular position, velocity, periodic motion, rolling without slipping, and angular acceleration.
• Next topic: rotational motion and momentum.