Dynamics Go Lecture Notes

Introduction

• Greetings: Jai Nepal!
• Topics for discussion:
  • Moment, Torque, and Equilibrium
  • Translational and Rotational Equilibrium
  • Solid Friction
  • Coefficient of Friction
  • Angle of Friction and Angle of Repose

Moment and Torque

• Definitions:
  • Moment/Torque: Effect of force applied in rotational motion.
  • Formula: Moment = Force × Perpendicular Distance from axis of rotation (τ = F × d)

Rotational Motion

• Rotational motion occurs when a force causes an object to rotate around an axis (e.g., opening a door).
• The axis of rotation is crucial for determining how much force is needed to create movement.

Understanding Moments

• Practical examples:
  • Opening a door requires less force if applied further from the hinge (axis of rotation).
  • A larger wrench provides more torque than a smaller one due to longer lever arm.
• Key Insight: Moment is constant; if the distance decreases, force must increase to maintain the same moment.

Scalar vs. Vector

• Moment: Scalar quantity (magnitude only).
• Torque: Vector quantity (magnitude and direction).
• Comparison: Momentum = mass × velocity, Moment = force × perpendicular distance.

Principle of Moments

• Statement: The sum of clockwise moments is equal to the sum of anti-clockwise moments around a given point, leading to equilibrium.

Equilibrium Concepts

Translational Equilibrium

• Condition: Net force acting on the body is zero.
• Definition: If external forces cancel each other out, the body is in a state of rest or uniform motion.

Rotational Equilibrium

• Condition: Net torque acting on the body is zero.
• If there's no net torque, the body remains in rest or uniform rotational motion.

Solid Friction

• Definition: Frictional force opposing motion between solid surfaces.
  • Always acts in the opposite direction to the applied force.
• Key Points:
  • Friction depends on the nature of the surfaces in contact.
  • More weight leads to more friction due to increased interlocking of surface atoms.

Coefficient of Friction

• Formula: μ = F_friction / R (where R is the normal reaction force).
• Understanding: Higher weight increases friction due to increased normal force.

Angle of Friction and Angle of Repose

• Angle of Repose: Minimum angle at which an object on an inclined surface begins to slide.
• Calculation: Can relate angle of repose to coefficient of friction using trigonometric functions (tan(θ) = F/N).

Conclusion

• Summary of key points regarding moment, torque, equilibrium, and friction.
• Understanding these concepts is crucial in dynamics and physical applications.
• Next lecture will cover additional topics in mechanics.