Center of Mass in Classes

Introduction

• Topic: System of Particles
• Main Idea: Center of Mass
• Purpose: Understanding the center of mass helps in comprehending collision theories.

What is Center of Mass?

• Example: Cricket ball example

  • Studying the center of mass of the ball is simpler while spinning it.
  • Studying individual particles is complex.

• Another Example: Projectile of a marker

  • When spinning a marker, its center of mass moves straight in the projectile.

Importance of Center of Mass

• Helps in understanding complex motion
• Using center of mass in Newton’s equations
  • Study of force and velocity of the center of mass in F = ma and P = mv.

Determination of Center of Mass

• Formula for center of mass:
  • Rcom = (m1 * r1 + m2 * r2) / (m1 + m2)
  • Different equations for x, y, z in 2D

Example

• Two masses m1 and m2 have a distance D between them.
  • Determine their position to study the center of mass.
  • How to find the center of mass of an entire rod or plate.

Discussion on Special Cases of Center of Mass

• Location of center of mass in evenly distributed mass.
• How to find center of mass in different shapes like: spherical, triangular, and hemispherical shapes.

Effect of Center of Mass on Motion

• How center of mass is affected if a mass is moved back and forth.
  • If a mass is moved 2 meters to the right, how should the other mass be moved to keep the center of mass position stable.

Conclusion

• Studying center of mass helps solve many problems in physics.
• Understanding principles of center of mass is essential for future chapters.

Additional Information

• Knowledge of center of mass is important for collision and rotation theories.
• Study of center of mass of different shapes will be covered in future lessons.

Note: These notes are for discussion on center of mass in classes and provide a strong foundation for future chapters.