Intro to Mechanics: Kinematics and Dynamics

Mechanics

Kinematics

• Study of motion without considering forces
• Describes the motion of objects in terms of position, velocity, and acceleration
• Key concepts:
  • Displacement: change in position (vector)
  • Distance: total length of path traveled (scalar)
  • Speed: rate of change of distance (scalar)
  • Velocity: rate of change of displacement (vector)
  • Acceleration: rate of change of velocity (vector)

Dynamics

• Study of motion considering forces
• Forces: pushes or pulls that cause objects to change their motion
• Key concepts:
  • Newton's First Law (Law of Inertia): an object at rest remains at rest, an object in motion remains in motion, unless acted upon by an external force
  • Newton's Second Law (F = ma): force is equal to the mass of an object multiplied by its acceleration
  • Newton's Third Law (Action-Reaction): every action has an equal and opposite reaction

Energy and Work

• Energy: ability to do work
• Types of energy:
  • Kinetic energy: energy of motion
  • Potential energy: energy of position or stored energy
  • Thermal energy: energy of heat
• Work: transfer of energy from one object to another through a force
• Key concepts:
  • Work-energy theorem: net work done on an object is equal to its change in kinetic energy
  • Conservation of energy: total energy remains constant in a closed system

Momentum

• Momentum: product of an object's mass and velocity
• Key concepts:
  • Conservation of momentum: total momentum remains constant in a closed system
  • Momentum is a vector quantity

Rotational Motion

• Study of motion around a fixed axis
• Key concepts:
  • Angular displacement: change in angular position (vector)
  • Angular velocity: rate of change of angular displacement (vector)
  • Angular acceleration: rate of change of angular velocity (vector)
  • Torque: rotational force that causes an object to rotate (vector)

Oscillations and Vibrations

• Study of repetitive motion around a fixed point
• Key concepts:
  • Period: time taken to complete one cycle of motion
  • Frequency: number of cycles per unit time
  • Amplitude: maximum displacement from the equilibrium position
  • Simple harmonic motion: oscillations that follow a sinusoidal pattern

Mechanics

Kinematics

• Motion is described in terms of position, velocity, and acceleration.
• Displacement is a change in position, a vector quantity.
• Distance is the total length of the path traveled, a scalar quantity.
• Speed is the rate of change of distance, a scalar quantity.
• Velocity is the rate of change of displacement, a vector quantity.
• Acceleration is the rate of change of velocity, a vector quantity.

Dynamics

• Forces are pushes or pulls that cause objects to change their motion.
• Newton's First Law: an object at rest remains at rest, an object in motion remains in motion, unless acted upon by an external force.
• Newton's Second Law: force is equal to the mass of an object multiplied by its acceleration (F = ma).
• Newton's Third Law: every action has an equal and opposite reaction.

Energy and Work

• Energy is the ability to do work.
• Kinetic energy is the energy of motion.
• Potential energy is the energy of position or stored energy.
• Thermal energy is the energy of heat.
• Work is the transfer of energy from one object to another through a force.
• Work-energy theorem: net work done on an object is equal to its change in kinetic energy.
• Conservation of energy: the total energy remains constant in a closed system.

Momentum

• Momentum is the product of an object's mass and velocity.
• Conservation of momentum: the total momentum remains constant in a closed system.
• Momentum is a vector quantity.

Rotational Motion

• Angular displacement is a change in angular position, a vector quantity.
• Angular velocity is the rate of change of angular displacement, a vector quantity.
• Angular acceleration is the rate of change of angular velocity, a vector quantity.
• Torque is a rotational force that causes an object to rotate, a vector quantity.

Oscillations and Vibrations

• Period is the time taken to complete one cycle of motion.
• Frequency is the number of cycles per unit time.
• Amplitude is the maximum displacement from the equilibrium position.
• Simple harmonic motion is oscillations that follow a sinusoidal pattern.