Fundamental Concepts of Classical Mechanics and Energy

Types of Motion

Uniform Rectilinear Motion (MRU)

The MRU definition is that the velocity vector remains constant. That is, the speed is constant in magnitude and direction.

Uniformly Accelerated Rectilinear Motion (MRUA)

The MRUA is motion where a body travels on a straight line maintaining a constant acceleration.

Uniform Circular Motion (UCM)

Uniform Circular Motion (UCM) is one in which a mobile describes a circle with constant angular velocity.

Uniformly Accelerated Circular Motion (UCMA)

Uniformly Accelerated Circular Motion (UCMA) is one in which the mobile moves in a circle with constant angular acceleration.

Fundamental Principles of Dynamics

Newton's Laws of Motion

First Law (Law of Inertia)

A body remains in its state of rest or Uniform Circular Motion (UCM) unless acted upon by a net external force, or if the resultant of forces acting is zero.

Second Law (Law of Dynamics)

If a resultant force acts on a body, it acquires an acceleration directly proportional to the applied force, the body's mass being the proportionality constant.

Third Law (Action and Reaction)

If a body exerts a force on another body ($F_{12}$), this, in turn, exerts a force on the first ($F_{21}$) with the same magnitude and direction, but opposite. $F_{12} = -F_{21}$.

Momentum and Impulse

We call momentum (or linear momentum) of a body the product of its mass times its velocity.

The resultant of all forces applied to a body is equal to the ratio of the change of its momentum and the time interval.

We call impulse of a force the product of the force by the time during which it acts.

The impulse of the force acting on a body is equal to the change of momentum of that body.

If the resultant of all external forces on a system is zero, the momentum of the system remains constant.

Types of Forces

We call normal force the force exerted by the bearing surface of a body on the body itself.

We call frictional force the force that appears at the contact surface of bodies, opposing the motion.

Centripetal force is the force that must be applied to a body to follow a circular path.

Work, Energy, and Conservation

Energy Definitions

Energy is the physical quantity by which bodies are able to make changes in themselves or other bodies.

The sources of energy are different resources that exist in nature from which humans can obtain usable energy in their activities.

Work

The work done by a constant force whose application point moves on a straight line is equal to the scalar product of the force and the displacement.

One joule (J) is the work done when a force of one newton (N) moves its point of application one meter (m) in the same direction as the force.

The total work done on a body is equal to the sum of the work done by each of the forces acting on that body.

Kinetic and Potential Energy

Kinetic energy is the capacity a body has to do work by virtue of being in motion.

The work done on a body by the resultant force is invested in changing its kinetic energy.

We call gravitational potential energy the energy possessed by bodies due to being a certain height above the surface of the Earth.

Mechanical Energy and Conservation

The mechanical energy of a body is the sum of its kinetic energy and potential energy.

If the only forces that perform work on an object are conservative forces, the mechanical energy of the body remains constant.