Physics: Kinematics and Dynamics

Kinematics

• Study of motion without considering forces
• Describes motion in terms of:
  • Displacement (distance from starting point)
  • Velocity (rate of change of displacement)
  • Acceleration (rate of change of velocity)
• Key concepts:
  • Position-time graphs
  • Velocity-time graphs
  • Acceleration-time graphs
  • Equations of motion:
    • v = u + at
    • s = ut + 0.5at^2
    • v^2 = u^2 + 2as

Dynamics

• Study of motion considering forces
• Forces:
  • Contact forces (normal force, friction, tension)
  • Non-contact forces (gravity, electromagnetic)
• Newton's Laws:
  1. First Law (Inertia): An object at rest remains at rest, an object in motion remains in motion, unless acted upon by an external force.
  2. Second Law (F = ma): Force is equal to the mass of an object multiplied by its acceleration.
  3. Third Law (Action-Reaction): For every action, there is an equal and opposite reaction.

Energy and Work

• Energy:
  • Kinetic energy (KE = 0.5mv^2)
  • Potential energy (PE = mgh)
• Work:
  • Done by a force on an object
  • Calculated by W = F × d
  • Unit: Joule (J)

Momentum

• Product of an object's mass and velocity
• Calculated by p = mv
• Conservation of momentum:
  • In closed systems, total momentum remains constant
  • Momentum is transferred from one object to another during collisions

Rotational Motion

• Rotational kinematics:
  • Angular displacement (θ)
  • Angular velocity (ω)
  • Angular acceleration (α)
• Rotational dynamics:
  • Torque (τ = r × F)
  • Rotational kinetic energy (KE = 0.5Iω^2)
  • Rotational inertia (I)

Oscillations and Vibrations

• Simple harmonic motion (SHM):
  • Periodic motion with constant acceleration
  • Examples: pendulum, spring-mass system
• Damped oscillations:
  • SHM with energy loss due to friction
  • Amplitude decreases with time

Kinematics

• Study of motion without considering forces
• Describes motion in terms of:
  • Displacement (distance from starting point)
  • Velocity (rate of change of displacement)
  • Acceleration (rate of change of velocity)
• Key concepts:
  • Position-time graphs: show the position of an object at different times
  • Velocity-time graphs: show the velocity of an object at different times
  • Acceleration-time graphs: show the acceleration of an object at different times
  • Equations of motion:
    • v = u + at: relates initial and final velocities, acceleration, and time
    • s = ut + 0.5at^2: relates displacement, initial velocity, acceleration, and time
    • v^2 = u^2 + 2as: relates initial and final velocities, acceleration, and displacement

Dynamics

• Study of motion considering forces
• Forces:
  • Contact forces: normal force, friction, tension
  • Non-contact forces: gravity, electromagnetic
• Newton's Laws:
  • First Law (Inertia): an object maintains its state of motion unless acted upon by an external force
  • Second Law (F = ma): force is proportional to the mass of an object and its acceleration
  • Third Law (Action-Reaction): every action has an equal and opposite reaction

Energy and Work

• Energy:
  • Kinetic energy (KE = 0.5mv^2): energy of motion
  • Potential energy (PE = mgh): energy of position
• Work:
  • Done by a force on an object, causing its displacement
  • Calculated by W = F × d, measured in Joules (J)

Momentum

• Product of an object's mass and velocity (p = mv)
• Conservation of momentum:
  • In closed systems, total momentum remains constant
  • Momentum is transferred from one object to another during collisions

Rotational Motion

• Rotational kinematics:
  • Angular displacement (θ): angle of rotation
  • Angular velocity (ω): rate of change of angular displacement
  • Angular acceleration (α): rate of change of angular velocity
• Rotational dynamics:
  • Torque (τ = r × F): rotational force that causes angular acceleration
  • Rotational kinetic energy (KE = 0.5Iω^2): energy of rotational motion
  • Rotational inertia (I): measures an object's resistance to rotational motion

Oscillations and Vibrations

• Simple harmonic motion (SHM):
  • Periodic motion with constant acceleration
  • Examples: pendulum, spring-mass system
• Damped oscillations:
  • SHM with energy loss due to friction
  • Amplitude decreases with time