Center of Mass in Classes

Introduction

• Subject: System of Particles
• Main Idea: Center of Mass
• Explanation: Understanding the center of mass will help in understanding the principles of collision.

What is Center of Mass?

• Example: Cricket Ball Example

  • It is easier to study the center of mass when throwing the ball.
  • Studying individual particles is complex.

• Another Example: Marker as a Projectile

  • When rotating the marker, its center of mass moves in a straight trajectory.

Importance of Center of Mass

• Helps in understanding complex motion
• Use of center of mass in Newton's equations
  • Studying force and velocity of 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)
  • In 2D, separate equations for x, y, z

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 a complete rod or plate.

Discussion on Special Cases of Center of Mass

• Position of center of mass on uniformly distributed mass.
• How to find the center of mass in different shapes such as spherical, triangular, and hemispherical.

Effect of Motion on Center of Mass

• If a mass is moved back and forth, how does the center of mass get affected?
  • If a mass is moved 2 meters to the right, how much should the other mass be shifted to keep the position of the center of mass stable?

Conclusion

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

Additional Information

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

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