Mechanics 101, part 1

Let's talk about basic classical mechanics since some folks may not be familiar with the precise meaning of some terminology I'll regularly use, or need a refresher.

Mechanics, or more specifically classical mechanics, is the part of physics that deals with the motion and reaction of objects under some influence (like a force). A ball bouncing, a vase sitting on a table, and a satellite orbiting Earth are all examples of classical mechanical systems. The fields of civil, mechanical and aeronautical engineering are concerned mainly with the application of classical mechanics, applied mechanics or engineering mechanics, and this is most of what will be discussed in this blog.

Within the field of applied mechanics, there are a number of sub-fields but the following are the most relevant to this blog:

• Statics: the field dealing with the study of bodies at rest
• Dynamics: the field dealing with the study of bodies in motion
• Mechanics of materials (or more generally: continuum mechanics): the field dealing with the behavior of deformable objects. When applied to solid materials, referred to as solid mechanics.

Now let's look at some important terms and concepts in classical mechanics. This is useful because some of the formal meanings of these words differ from their common usages.

UPDATE 27 Nov: I added a quick definition of displacement, strength, stiffness and hardness.

• Mass: mass is essentially the measure of how much stuff is in an object. Units for this include grams (g), kilograms (kg), pounds (lbs).
• Position: position is the location of some point in space relative to some reference point. It is a vector quantity, having both magnitude and direction (e.g., 3 feet above my laptop and 1 foot to the left). Units are the same as units of length: meter (m), foot (ft), etc.
• Displacement: displacement the change in position from one point in time to the next. It is also a vector quantity, having both magnitude and direction (e.g. the thing moved 2 feet to the left).
• Velocity: velocity is the rate of change of the position of an object with time. It is a vector quantity, having both magnitude and direction (e.g., 10 mph upward). The magnitude of the velocity vector is also known as the speed.  Units include meter per second (m/s), kilometer per hour (kph or km/hr), miles per hour (mph or mi/hr).  
• Acceleration: acceleration is the rate of change of the velocity of an object with time. It is a vector quantity, having both magnitude and direction (e.g., 1 m/s\(^2\) upward). Units include meter per second squared (m/s\(^2\)) or more awkwardly but identical: meter per second per second, ((m/s)/s).
• Force: a force is an action on an object that tends to cause a change in speed, direction, shape or size. Newton's second law (\(F = ma\)), states that the acceleration, a, of an object under a given net force, F, is inversely proportional to its mass, m. In short: higher mass, less acceleration for the same force. Units of force include Newtons (N), kilograms-force (kg-f) and pounds-force (lbs-f).
• Weight: weight is a special case of a force, and is generally taken to refer to the force on an object due to the acceleration by gravity. Mass and weight are sometimes used interchangeably in speaking (such as referring to a 5 lb hanging mass, when really the object being called a hanging mass weighs 5 lbs.), but they are different concepts in mechanics.
• Torque: a torque (sometimes called a moment of force or just moment) is a special case of a force which acts to cause a rotation of an object about a given axis. It can be resolved into a force tangential to the rotation at a given distance and has units of force*distance such as N*m.
• Mass Moment of Inertia: the mass moment of inertia for an object is its intrinsic resistance to a rotational acceleration (i.e. resistance because of its mass, not because of friction, etc.). It is analogous to the mass resisting a linear acceleration caused by an applied force. It has units of the form mass*distance^2, such as kg*m\(^2\).
• Energy: energy is one of the basic properties of a physical system, like mass or position. There are a number of types of energy, but we'll be mainly concerned with kinetic energy (associated with moving objects) and potential energy (associated with the position or arrangement of the system). Energy has its own units, such as Joules (J), which is the equivalent to kg*(m\(^2\)/s\(^2\)).
• Momentum: momentum is the product of the velocity of an object and its mass: \(P = mV\), and has units that include kg*m/s.
• Equilibrium: In mechanics, equilibrium generally refers to mechanical equilibrium, the condition that the sum of all applied forces and torques acting on an object is zero. This implies that the body is either not moving or is travelling at a constant velocity.
• Stress: stress is a measure of the forces exerted between neighboring particles in a continuous body. It is defined as the force being exerted by neighboring particles per unit area separating them. There are two major types: Normal (force perpendicular to the area) and shear (force parallel to the area). For example, the normal stress, \(\sigma\), on a bar of cross sectional area, A, with an applied normal load, P, is \(\sigma = P/A\). Units are of the form force per unit area, such as N/m\(^2\), which is equivalent to the Pascal (Pa).
• Strain: strain is a measure of the deformation of a body relative to some reference. For example, the change in length of a stretched bar vs its original length: \(\epsilon = \Delta L/L\). This measure is unitless.
• Area Moment/Area Moment of Inertia: a measure of the distribution of points in an area with respect to a given axis. This is purely a geometric measure, and should not to be confused with the mass moment of inertia.
• Strength: The amount of stress a body can support before failing. Examples: Yield strength is the stress a body can support before yielding. Fracture strength is the stress a body can support before fracturing. Strength is a point along the stress-strain curve for a material and applies to bulk deformation.
• Hardness: A measure of the amount of stress required for localized plastic deformation such as an indentation or scratch. This can often be correlated to the yield strength for metals, particularly steels.
• Stiffness: The amount of change in load that results from a given deformation increment. Stiffness is the slope of the force-displacement or stress-strain curve. The stiffness of the linear elastic portion of a stress-strain curve is called the Young's modulus.

My next posts will talk more about statics, dynamics and mechanics of materials.