Dynamics is the study of forces and their effect on motion.

Newton's Laws of Motion

• First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion with constant velocity unless acted upon by a net external force.
• Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
  • F = ma
• Third Law: For every action, there is an equal and opposite reaction. Forces always occur in pairs.

Types of Forces

• Contact Forces: Require physical contact (normal force, friction, tension, applied force)
• Non-Contact Forces: Act at a distance (gravity, electric, magnetic)

Gravity and Kepler's Laws:

Universal Law of Gravitation:

• F = G(m₁m₂)/r²

Kepler's Laws (planetary motion):

• Planets orbit in ellipses with the Sun at one focus
• Planets sweep equal areas in equal times
• T² ∝ r³ (period squared proportional to radius cubed)

Net Force and Centripetal Acceleration

• Net Force (ΣF): Vector sum of all forces acting on an object
• Centripetal Acceleration: Acceleration directed toward the center of circular motion
  • ac = v²/r
  • Fc = mv²/r

Variables:

• F=force