Physics Chapter on Newton's Laws and Friction

Newton's Laws

• Newton's First Law: An object at rest stays at rest, and an object in motion stays in motion with constant velocity (in magnitude and direction) if no net force acts on it.

• Newton's Second Law: The net force acting on an object is equal to the product of its mass and acceleration.

  • ΣF = ma
  • Acceleration's direction is the same as the net force's direction.
  • Component form: ΣFx = max, ΣFy = may, ΣFz = maz

Newton's Third Law

• Newton's Third Law: For every action, there is an equal and opposite reaction. If an object exerts a force on a second object, the second object exerts an equal but opposite force on the first object.

Friction

• Friction: When surfaces slide over each other, each exerts a frictional force parallel to the surfaces. This force opposes the relative motion.

• Self-Adjusting Force: Friction can adjust its magnitude to any value between zero and the maximum limiting value.

  • 0 ≤ f ≤ fmax

• Types of Friction:

  • Static friction (fs): Acts when there's no relative motion.

    • fs ≤ μsN, where μs is the coefficient of static friction and N is the normal force.

  • Kinetic friction (fk): Acts when there is relative motion.

    • fk = μkN, where μk is the coefficient of kinetic friction and N is the normal force.

Laws of Friction

• Limiting Friction: The maximum force of friction, proportional to the normal force, and independent of the contact area.
  • fmax = μN

Properties of Friction

• Static Friction at Rest: If a body's at rest, static friction is parallel to the surface and equal in magnitude to the external force. If the external force increases, then static friction increases.

• Maximum Static Friction: The maximum value of static friction is given by:

  • fs(max) = μsN (μs is the coefficient of static friction, N is the magnitude of the normal force)

• Static to Kinetic: If the external force is greater than fs(max), the body begins to slide, and kinetic friction takes over.

• Kinetic Friction: The magnitude of kinetic friction is constant fk = μkN (μk is the coefficient of kinetic friction)

Angle of Repose

• Angle of Repose: The minimum angle of inclination of an inclined plane at which a body placed on it begins to slide down.

• Mathematical Relation: tan ø = μs ( ø is the angle of repose, μs is the coefficient of static friction)

Centripetal Force

• Centripetal Acceleration: A particle moving in a circular path at constant speed experiences a centripetal acceleration that's directed towards the center of the circle: ac = v^2/r.

• Tangential Acceleration: If there's angular acceleration, the particle's speed changes, leading to a tangential acceleration at: at = αr

  • The net acceleration is the vector sum of centripetal and tangential accelerations.