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Lecture on Inertia

Jul 12, 2024

Lecture on Inertia

What is Inertia?

  • Inertia: The tendency of an object to resist changes in its state of motion.
  • Newton's First Law:
    • An object in motion will continue in motion, and an object at rest will remain at rest unless acted on by a net force.

Properties of Inertia

  • Rest: An object at rest remains at rest.
  • Motion: A moving object wants to keep moving unless acted on by net force or friction.
  • Mass Relation: Inertia is a property that resists changes to an object's state of motion.
  • Example:
    • Object with mass of 10 kg and another with 100 kg.
    • Both subjected to 50 N force.
    • Heavier object (100 kg) has more inertia and is harder to move.

Newton's Second Law

  • Formula: Net Force = Mass x Acceleration (F = ma)
  • Examples:
    • Object 1: Mass = 10 kg, Force = 50 N
      • Acceleration = 50 / 10 = 5 m/s²
    • Object 2: Mass = 100 kg, Force = 50 N
      • Acceleration = 50 / 100 = 0.5 m/s²
    • Conclusion: The smaller object has larger acceleration = less inertia. Larger object has smaller acceleration = more inertia.
  • Proportionality: Inertia is proportional to mass.

Rotational Motion & Inertia

  • Two Objects Comparison:
    • Thin Hoop: Mass at the edge.
    • Solid Disc: Mass distributed throughout.
  • Example:
    • Mass = 10 kg for both, Radius = 2 m for both.
    • Same tension force applied.
    • Thin hoop has more inertia than solid disc due to mass distribution.

Calculations for Rotational Inertia

  • Inertia of Thin Hoop: I = mr²
  • Inertia of Solid Disc: I = 0.5 * mr²
  • Inertia of Sphere: I = 0.4 * mr²
  • Key Point: Distribution of mass impacts inertia.
    • Mass away from rotation axis = increased inertia.
    • Mass closer to rotation axis = decreased inertia.
  • Equations:
    • Torque (Ï„) = Inertia (I) x Angular acceleration (α)
    • Translational: F = ma
    • Rotational: Ï„ = Iα

Understanding Torque and Angular Variables

  • Torque (Ï„): Rotational equivalent of force.
  • Angular acceleration (α): Rotational equivalent of linear acceleration.
  • Mass (m): Proportional to inertia in both types of motion.

Summary

  • Inertia = mass × resistance to changes in motion.
  • Translational Motion: F = ma
  • Rotational Motion: Ï„ = Iα
  • Different objects have different inertia based on mass and distribution.

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