Motion (physics)

In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of velocity, acceleration, displacement and time.^[1] Motion is observed by attaching a frame of reference to a body and measuring its change in position relative to another reference frame.

A body which does not move is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in a closed system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum.

As there is no absolute frame of reference, absolute motion cannot be determined.^[2] Thus, everything in the universe can be considered to be moving.^[3]

More generally, the term motion refers to a parameterized change in position of components of a physical system. For example, one can talk about motion of a wave or a quantum particle (or any other field).

Contents 1 Laws of motion 1.1 Classical mechanics 1.2 Quantum mechanics 2 Kinematics 2.1 Planar motion 2.2 Spherical motion 2.3 Spatial motion 3 List of "imperceptible" human motions 3.1 Universe 3.2 Galaxy 3.3 Solar System 3.4 Earth 3.5 Continents 3.6 Internal body 3.7 Cells 3.8 Particles 3.9 Subatomic particles 4 Light 5 Types of motion 6 References

Laws of motion

In physics, motion in the universe is described through two sets of apparently contradictory laws of mechanics. Motions of all large scale and familiar objects in the universe (such as projectiles, planets, cells, and humans) are described by classical mechanics. Whereas the motion of very small atomic and sub-atomic objects is described by quantum mechanics.

Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. It produces very accurate results within these domains, and is one of the oldest and largest subjects in science, engineering and technology.

Classical mechanics is fundamentally based on Newton's Laws of Motion. These laws describe the relationship between the forces acting on a body and the motion of that body. They were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, first published on July 5, 1687. His three laws are:

1. In the absence of a net external force, a body either is at rest or moves with constant velocity.
2. The net external force on a body is equal to the mass of that body times its acceleration; F = ma. Alternatively, force is proportional to the time derivative of momentum.
3. Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction.^[4]

Newton's three laws of motion, along with his law of universal gravitation, explain Kepler's laws of planetary motion, which were the first to accurately provide a mathematical model or understanding orbiting bodies in outer space. This explanation unified the motion of celestial bodies and motion of objects on earth.

Classical mechanics was later further enhanced by Albert Einstein's special relativity and general relativity. Special relativity explains the motion of objects with a high velocity, approaching the speed of light; general relativity is employed to handle gravitation motion at a deeper level.

Quantum mechanics

Quantum mechanics is a set of principles describing physical reality at the atomic level of matter (molecules and atoms) and the subatomic (electrons, protons, and even smaller particles). These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation energy, this described in the wave–particle duality.

In contrast to classical mechanics, where accurate measurements and predictions can be calculated about location and velocity, in the quantum mechanics of a subatomic particle, one can never specify its state, such as its simultaneous location and velocity, with complete certainty (this is called the Heisenberg uncertainty principle).

In addition to describing the motion of atomic level phenomena, quantum mechanics is useful in understanding some large scale phenomenon such as superfluidity, superconductivity, and biological systems, including the function of smell receptors and the structures of proteins.

Kinematics

Kinematics applies geometry to the analysis of movement, or motion, of a mechanical system.^[5] The rotation and sliding movement central a mechanical system is modeled mathematically as Euclidean, or rigid, transformations. The set of rigid transformations in three dimensional space forms a Lie group, denoted as SE(3).

Planar motion

While all motion in a mechanical system occurs in three dimensional space, planar motion can be analyzed using plane geometry, if all point trajectories are parallel to a plane. In this case the system is called a planar mechanism (or robot). The kinematic analysis of planar mechanisms uses the subset of SE(3) consisting of planar rotations and translations, denoted SE(2).

The group SE(2) is three dimensional, which means that every position of a body in the plane is defined by three parameters. The parameters are often the x and y coordinates of the origin of a coordinate frame in M measured from the origin of a coordinate frame in F, and the angle measured from the x-axis in F to the x-axis in M. This is described saying a body in the plane has three degrees-of-freedom. SE(2) is the configuration space for a planar body, and a planar motion is a curve in this space.

Spherical motion

It is possible to construct a mechanical system such that the point trajectories in all components lie in concentric spherical shells around a fixed point. An example is the gimbaled gyroscope. These devices are called spherical mechanisms.^[6] Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge passes through the same point. This point becomes center of the concentric spherical shells. The movement of these mechanisms is characterized by the group SO(3) of rotations in three dimensional space. Other examples of spherical mechanisms are the automotive differential and the robotic wrist.

Select this link for an animation of a Spherical deployable mechanism.

The rotation group SO(3) is three dimensional. An example of the three parameters that specify a spatial rotation are the roll, pitch and yaw angles used to define the orientation of an aircraft. SO(3) is the configuration space for a rotating body, and a spherical motion is a curve in this space.

Spatial motion

A mechanical system in which a body moves through a general spatial movement is called a spatial mechanism. An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends, also called spherical joints or ball joints. The rod ends allow the input and output cranks of the RSSR linkage to be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms, Stewart platforms, and humanoid robotic systems are also examples of spatial mechanisms.

Select this link for an animation of Bennett's linkage, which is a spatial mechanism constructed from four hinged joints.

The group SE(3) is six dimensional, which means the position of a body in space is defined by six parameters. Three of the parameters define the origin of the moving reference frame relative to the fixed frame. Three other parameters define the orientation of the moving frame relative to the fixed frame. SE(3) is the configuration space for a body moving in space, and a spatial motion is a curve in this space.

List of "imperceptible" human motions

Humans, like all things in the universe are in constant motion,^[7] however, aside from obvious movements of the various external body parts and locomotion, humans are in motion in a variety of ways which are more difficult to perceive. Many of these "imperceptible motions" are only perceivable with the help of special tools and careful observation. The larger scales of "imperceptible motions" are difficult for humans to perceive for two reasons: 1) Newton's laws of motion (particularly Inertia) which prevent humans from feeling motions of a mass to which they are connected, and 2) the lack of an obvious frame of reference which would allow individuals to easily see that they are moving.^[8] The smaller scales of these motions are too small for humans to sense.

Universe

• Spacetime (the fabric of the universe) is actually expanding. Essentially, everything in the universe is stretching like a rubber band. This motion is the most obscure as it is not physical motion as such, but rather a change in the very nature of the universe. The primary source of verification of this expansion was provided by Edwin Hubble who demonstrated that all galaxies and distant astronomical objects were moving away from us ("Hubble's law") as predicted by a universal expansion.^[9]

Galaxy

• The Milky Way Galaxy, is hurtling through space at an incredible speed. It is powered by the force left over from the Big Bang. Many astronomers believe the Milky Way is moving at approximately 600 km/s relative to the observed locations of other nearby galaxies. Another reference frame is provided by the Cosmic microwave background. This frame of reference indicates that The Milky Way is moving at around 552 km/s.^[10]

Solar System

• The Milky Way is rotating around its dense galactic center, thus the solar system is moving in a circle within the galaxy's gravity. Away from the central bulge or outer rim, the typical stellar velocity is between 210 and 240 km/s (about half-million mi/h).^[11]

Earth

• The Earth is rotating or spinning around its axis, this is evidenced by day and night, at the equator the earth has an eastward velocity of 0.4651 km/s (1040 mi/h).^[12]
• The Earth is orbiting around the Sun in an orbital revolution. A complete orbit around the sun takes one year or about 365 days; it averages a speed of about 30 km/s (67,000 mi/h).^[13]

Continents

• The Theory of Plate tectonics tells us that the continents are drifting on convection currents within the mantle causing them to move across the surface of the planet at the slow speed of approximately 1 inch (2.54 cm) per year.^[14][15] However, the velocities of plates range widely. The fastest-moving plates are the oceanic plates, with the Cocos Plate advancing at a rate of 75 mm/yr^[16] (3.0 in/yr) and the Pacific Plate moving 52–69 mm/yr (2.1–2.7 in/yr). At the other extreme, the slowest-moving plate is the Eurasian Plate, progressing at a typical rate of about 21 mm/yr (0.8 in/yr).

Internal body

• The human heart is constantly contracting to move blood throughout the body. Through larger veins and arteries in the body blood has been found to travel at approximately 0.33 m/s.^[17] Though considerable variation exists, and peak flows in the venae cavae have been found between 0.1 m/s and 0.45 m/s.^[18]
• The smooth muscles of hollow internal organs are moving. The most familiar would be peristalsis which is where digested food is forced throughout the digestive tract. Though different foods travel through the body at rates, an average speed through the human small intestine is 2.16 m/h (0.036 m/s).^[19]
• Typically some sound is audible at any given moment, when the vibration of these sound waves reaches the ear drum it moves in response and allows the sense of hearing.
• The human lymphatic system is constantly moving excess fluids, lipids, and immune system related products around the body. The lymph fluid has been found to move through a lymph capillary of the skin at approximately 0.0000097 m/s.^[20]

Cells

The cells of the human body have many structures which move throughout them.

• Cytoplasmic streaming is a way which cells move molecular substances throughout the cytoplasm.^[21]
• Various motor proteins work as molecular motors within a cell and move along the surface of various cellular substrates such as microtubuless. Motor proteins are typically powered by the hydrolysis of adenosine triphosphate (ATP), and convert chemical energy into mechanical work.^[22] Vesicles propelled by motor proteins have been found to have a velocity of approximately 0.00000152 m/s.^[23]

Particles

• According to the laws of thermodynamics all particles of matter are in constant random motion as long as the temperature is above absolute zero. Thus the molecules and atoms which make up the human body are vibrating, colliding, and moving. This motion can be detected as temperature; higher temperatures, which represent greater kinetic energy in the particles, feel warm to humans whom sense the thermal energy transferring from the object being touched to their nerves. Similarly, when lower temperature objects are touched, the senses perceive the transfer of heat away from the body as feeling cold.^[24]

Subatomic particles

• Within each atom, electrons exist in an area around the nucleus. This area is called the electron cloud. According to Bohr's model of the atom, electrons have a high velocity, and the larger the nucleus they are orbiting the faster they would need to move. If electrons 'move' about the electron cloud in strict paths the same way planets orbit the sun, then electrons would be required to do so at speeds which far exceed the speed of light. However, there is no reason that one must confine one's self to this strict conceptualization, that electrons move in paths the same way macroscopic objects do. Rather one can conceptualize electrons to be 'particles' that capriciously exist within the bounds of the electron cloud.^[25]
• Inside the atomic nucleus the protons and neutrons are also probably moving around due the electrical repulsion of the protons and the presence of angular momentum of both particles.^[26]

Light

Light propagates at 299,792,458 m/s, often approximated as 300,000 kilometres per second or 186,000 miles per second. The speed of light (or c) is the speed of all massless particles and associated fields in a vacuum, and it is believed to be the upper limit on the speed at which energy, matter, and information can travel.

Types of motion

• Simple harmonic motion – (e.g. pendulum).
• Linear motion – motion which follows a straight linear path, and whose displacement is exactly the same as its trajectory.
• Reciprocating (i.e. vibration)
• Brownian motion (i.e. the random movement of particles)
• Circular motion (e.g. the orbits of planets)
• Rotary motion – a motion about a fixed point ex. the wheel of a bicycle
• Curvilinear motion – It is defined as the motion along a curved path that may be planar or in three dimensions.
• Rotational motion - (e.g. Ferris wheel)

References

Kinematics ← Integrate … Differentiate → Displacement (Distance) | Velocity (Speed) | Acceleration | Jerk | Jounce