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Forces and Motion on Rigid and Non-Rigid Bodies

May 30, 2024

Forces and Motion on Rigid and Non-Rigid Bodies

Effects of Force on Bodies

Rigid Bodies:

  1. Behavior under Force:
    • If pivoted: Rotatory motion (Turning Motion)
    • If non-pivoted: Linear or Translational motion

Non-Rigid Bodies:

  1. Behavior under Force:
    • Shape change
    • Size change
    • Structure change

Types of Motion

Rigid Bodies:

  1. Pivoted:
    • Rotatory Motion
  2. Non-Pivoted:
    • Linear or Transitional Motion

Non-Rigid Bodies:

  1. Under Force:
    • Deformation: Changes in shape, size, and structure

Turning Effect of Force

Definition:

  • When a force is applied on a rigid body that is pivoted, causing it to rotate.

Terms:

  • Also known as Moment of Force or Torque
  • Formula: $$ \text{Moment of Force} = \text{Force} \times \text{Perpendicular Distance} $$

Example:

  • A door with hinge (pivoted): Applying a force away from the hinge results in rotation.

Calculating Moment of Force

  • Formula: Force × Perpendicular Distance from the pivot point
  • Unit: Newton-meter (Nm) or Joule
  • Vector Quantity: Must consider direction (Clockwise is negative, Anti-clockwise is positive)
  • Examples:
    • Uniform meter rule with different forces at various points
    • Balancing weights on a seesaw

Special Cases of Moment of Force

  • Maximizing Turning Effect: Increase the force or perpendicular distance
  • Zero Moment of Force: When either force or perpendicular distance is zero, or when force passes through the pivot point

Equilibrium

Conditions for Equilibrium:

  • Net Force = 0 (Transitional Equilibrium)
  • Net Moment of Force = 0 (Rotational Equilibrium)
  • Types: Static (rest) and dynamic (motion)

Principle of Moment of Force:

  • At equilibrium, sum of clockwise moment = sum of anti-clockwise moment

Center of Gravity (CG)

Definition:

  • The point where the net moment of force of the weights of all the particles constituting the body is zero.
  • Factors influencing CG: Mass distribution, shape, size, and structure

Characteristics:

  • Can lie outside the body (e.g., ring)
  • Changes with deformation of the body

Examples of CG Location:

  • Uniform rod: at the midpoint
  • Triangular object: base-dependent location

Uniform Circular Motion

Features:

  • Speed is constant, but direction changes leading to change in velocity
  • Results in centripetal acceleration
  • Centripetal Force: Net force towards the center, responsible for circular motion

Formula for Centripetal Force:

  • $$ F_{centripetal} = \frac{mv^2}{r} $$
  • Examples: Earth's orbit around the Sun, electron's orbit around nucleus

Centrifugal Force

Definition:

  • An apparent force experienced in a rotating frame of reference, directed away from the center
  • Real vs. Pseudo Forces:
    • Centripetal force is real
    • Centrifugal force is a pseudo or fictitious force

Example Scenario:

  • Observer in a rotating giant wheel perceives an outward force (centrifugal) balancing the inward centripetal force

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