Lecture Notes on Centripetal and Centrifugal Forces

Introduction

• Centripetal force appears strange at first glance.
• Example: Moon revolves around Earth.

Understanding Centripetal Force

• The force must be perpendicular to the velocity for circular motion.
• In mechanics, velocity is usually in the direction of the applied force.
• Centripetal force is an exception; it is perpendicular to velocity.

Thought Experiment with a Tennis Ball

• Initial motion is a straight line.
• Applying force perpendicular to motion changes the direction.
• Repeating this process results in a shape close to a circle.
• If force is applied continuously in the perpendicular direction, the object moves in a circle.
• Key conclusion: More centripetal force leads to greater deflection or lesser radius of the circle.

Deriving Centripetal Force

• Approach should be analytical, starting with Newton's definition of force.
• However, an animated method can provide better conceptual understanding.
• Key Equation: Lesser the radius, more centripetal force is required.
• Examples of centripetal force sources:
  • Gravitational force (e.g., Moon-Earth system)
  • Tension in a string (e.g., rotating object)
  • Frictional force (e.g., spinning wooden block)

Understanding Centrifugal Force

• Centrifugal Force: Is it real?
• Examples:
  • Fluid spins in a beaker; fluid flows outward.
  • Centrifugal casting process: molten metal moves to outer wall.
  • Suspended ball travels outward as speed increases.
• Scientifically, centrifugal force is a pseudo force.
  • Rotating objects need a radially inward force (centripetal force).
  • Centrifugal force is used in non-inertial frames of reference for analysis.

Analyzing Examples with Centripetal Force

• As the ball rotates faster, it moves outward.
• The tension in the rope provides the necessary centripetal force.
• Tension has two components:
  • Horizontal component provides centripetal force.
  • Vertical component balances weight of the ball.
• As rotation increases, tension must also increase, leading to an increased angle of the rope.

Rotating Fluid Example

• Each fluid particle needs centripetal force for circular motion.
• Pressure differences across water levels generate the required centripetal force.
• As rotation speed increases, particles at outer radius need more centripetal force.
• Result: The fluid surface curves rather than remains straight.

Conclusion

• Avoid using centrifugal force in scientific or engineering analyses.
• Focus on centripetal force, which is the actual force required for a rotating object.