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Unit 1: Non inertial Systems & Fictitious Forces | BSc Physics Notes | Kannur University | Semester 3

noninertial systems, fictitious forces, BSc physics, centrifugal force, coriolis force, kannur university physics, classical mechanics, pseudo forces
Sreehari K

 

Unit 1: Non inertial Systems & Fictitious Forces | BSc Physics Notes | Kannur University | Semester 3



This unit introduces Non inertial reference frames, explaining how they differ from inertial frames and why fictitious forces such as the Coriolis force and centrifugal force appear in accelerating frames. It explores real-life applications like rotating Earth systems, weather patterns, and motion in elevators. The physics of rotating frames, translating frames, and the dynamics under pseudo forces are simplified for clear conceptual understanding. Essential for Kannur University BSc Physics students, this topic bridges classical mechanics with real-world phenomena. Learn how Newton’s laws are modified in Non inertial frames, enhancing your grasp of motion under acceleration. Perfect for exam preparation, conceptual clarity, and competitive physics exams.




Semester 3 | Kannur University | Notes | BSc Physics

Unit 1:  Non inertial Systems and Fictious Forces: Link
Unit 2:  Central Force Motions: Link
Unit 3:  Harmonic Oscillator: Link
Unit 4:  Waves: Link

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Here’s a clear diagram illustrating the key concepts—such as fictitious forces in accelerating systems and rotating frames—which should help you visualize and better understand the topic.

Unit 1: Non-Inertial Systems & Fictitious Forces

BSc Physics (Kannur University – Semester 3)

1. Overview & Syllabus Highlights

  • Curriculum coverage: According to the Kannur University syllabus, this unit spans approximately 12 lecture hours, covering:

    • Galilean transformations

    • Uniformly accelerating systems and apparent gravity

    • Pendulum behavior in an accelerating car

    • Principle of equivalence

    • Rotating coordinate systems and fictitious forces

    • Coriolis force and deflection effects on rotating Earth
      (payyanurcollege.ac.in, Kannur University)

2. Key Concepts & Definitions

a) Inertial vs Non-Inertial Frames

  • Inertial frame: A reference frame moving at constant velocity (or at rest); Newton’s laws apply directly.

  • Non-inertial frame: One that's accelerating or rotating. Within such frames, Newton’s laws appear violated unless fictitious (pseudo) forces are introduced.
    (Physics LibreTexts, Wikipedia)

b) Fictitious (Pseudo) Forces

  • These are apparent forces with no physical source—they arise due to the acceleration of the reference frame itself.

  • Examples:

    • Centrifugal Force – pushes outward in rotating systems

    • Coriolis Force – causes deflection when moving in rotating frames

    • Euler Force – emerges when angular velocity changes
      (Wikipedia)

c) Rotating Frames & Mathematical Expressions

Inside a rotating frame (angular velocity ω), Newton’s second law becomes modified to include fictitious force terms:

F′=F−mdωdt×r′−2m ω×v′−m ω×(ω×r′)=ma′\mathbf{F'} = \mathbf{F} - m \frac{d\boldsymbol{\omega}}{dt} \times \mathbf{r}' - 2m \, \boldsymbol{\omega} \times \mathbf{v}' - m\, \boldsymbol{\omega} \times (\boldsymbol{\omega} \times \mathbf{r}') = m \mathbf{a}'

Here, the three additional terms represent:

  • Euler force: −mdωdt×r′-m \frac{d\boldsymbol{\omega}}{dt} \times \mathbf{r}'

  • Coriolis force: −2m ω×v′-2m\,\boldsymbol{\omega} \times \mathbf{v}'

  • Centrifugal force: −m ω×(ω×r′)-m\,\boldsymbol{\omega} \times (\boldsymbol{\omega} \times \mathbf{r}')
    (Wikipedia)

3. Applications & Examples

a) Accelerating Frames (e.g., a Car)

  • In a car accelerating rightward, a passenger feels pushed left—this is not a real force, but a pseudo-force invoked to apply Newton’s law in the car’s non-inertial frame.

  • In the inertial (ground) frame, there is no force pushing the passenger; it's inertia keeping their motion straight.
    (Physics LibreTexts, Fiveable)

b) Pendulum in an Accelerating Car

  • A pendulum hanging in a car tilts backward due to the pseudo force mAmA (where AA is acceleration), resembling a gravitational pull opposite to the acceleration.
    (Kannur University)

c) Rotating Systems (e.g., Merry-Go-Round, Weather Patterns)

  • Centrifugal force explains why riders feel pushed outward in a rotating frame.

  • Coriolis force explains deflections:

    • Rightward in Northern Hemisphere

    • Leftward in Southern Hemisphere

    • This deflection is critical in meteorology, influencing storm rotation and air current patterns.
      (Physics LibreTexts, Wikipedia, UH Pressbooks)

4. Sample Notes Outline

A. Introduction

  • Explain inertial vs non-inertial frames.

  • The necessity of fictitious forces.

B. Types of Fictitious Forces

  • Centrifugal

  • Coriolis

  • Euler

C. Acceleration in Rotating Systems

  • How acceleration transforms between frames

  • Equations and terms

D. Real-World Examples

  • Accelerating car and pendulum tilt

  • Merry-go-round ride

  • Deflection of falling objects due to Coriolis force

  • Storm rotations (cyclones/hurricanes)

E. Practice Problems

  • Determine pendulum tilt angle in accelerating cart

  • Calculate effective forces on particles in rotating frames

  • Sketch and analyze deflection paths due to Coriolis force

5. Study Tips

  • Start with clear definitions of frames and forces.

  • Use diagrams (like the one above) to visualize scenarios.

  • Practice transforming Newton’s second law between frames.

  • Apply formulas to real-life problems—pendulum, weather systems, rotating devices.


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