Intro to Mechanics: Kinematics and Dynamics

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)

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: 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: 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

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)

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

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.

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 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 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.

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.