Physics Mechanics: Kinematics and Dynamics

Mechanics

Kinematics

• Study of motion without considering forces
• Descriptive quantities:
  • Position (x)
  • Displacement (Δx)
  • Velocity (v)
  • Acceleration (a)
• Kinematic equations:
  • v = Δx / Δt
  • a = Δv / Δt
  • x = x0 + v0t + (1/2)at^2

Dynamics

• Study of motion considering forces
• Newton's Laws:
  1. First Law (Inertia): An object at rest remains at rest, and an object in motion remains in motion, unless acted upon by an external force.
  2. Second Law (Force and Acceleration): F = ma (Force equals mass times acceleration)
  3. Third Law (Action and Reaction): For every action, there is an equal and opposite reaction

Work and Energy

• Work: W = F × d (Force times displacement)
• Kinetic Energy: KE = (1/2)mv^2 (Energy of motion)
• Potential Energy: PE = mgh (Energy of position)
• Conservation of Energy: The total energy of a closed system remains constant (KE + PE = constant)

Momentum

• Linear Momentum: p = mv (Mass times velocity)
• Conservation of Momentum: The total momentum of a closed system remains constant (p = constant)

Rotational Motion

• Angular Displacement: Δθ (Change in angular position)
• Angular Velocity: ω = Δθ / Δt (Angular velocity)
• Angular Acceleration: α = Δω / Δt (Angular acceleration)
• Torque: τ = r × F (Rotational force)

Mechanics

Kinematics

• The study of motion without considering forces, focusing on descriptive quantities such as position, displacement, velocity, and acceleration.
• Position (x) is a measure of an object's location, while displacement (Δx) is the change in position.
• Velocity (v) is the rate of change of position, and acceleration (a) is the rate of change of velocity.
• Kinematic equations describe the relationships between these quantities, including v = Δx / Δt, a = Δv / Δt, and x = x0 + v0t + (1/2)at^2.

Dynamics

• The study of motion considering forces, based on Newton's Laws.
• The First Law (Inertia) states that an object at rest remains at rest, and an object in motion remains in motion, unless acted upon by an external force.
• The Second Law (Force and Acceleration) states that force (F) equals mass (m) times acceleration (a), or F = ma.
• The Third Law (Action and Reaction) states that for every action, there is an equal and opposite reaction.

Work and Energy

• Work is the product of force and displacement, or W = F × d.
• Kinetic Energy is the energy of motion, given by KE = (1/2)mv^2, where m is mass and v is velocity.
• Potential Energy is the energy of position, given by PE = mgh, where m is mass, g is gravity, and h is height.
• The Conservation of Energy states that the total energy of a closed system remains constant, with kinetic energy and potential energy being interchangeable.

Momentum

• Linear Momentum is the product of mass and velocity, or p = mv.
• The Conservation of Momentum states that the total momentum of a closed system remains constant, with momentum being conserved in collisions.

Rotational Motion

• Angular Displacement is the change in angular position, or Δθ.
• Angular Velocity is the rate of change of angular displacement, or ω = Δθ / Δt.
• Angular Acceleration is the rate of change of angular velocity, or α = Δω / Δt.
• Torque is the rotational force that causes angular acceleration, or τ = r × F.