Dynamics (mechanics)

Dynamics is the branch of mechanics that deals with the motion of bodies under the action of forces. This includes both kinematics, which is the study of motion of objects without concern about the causes of motion, and kinetics, which is concerned with studying the effects of forces of motion. Dynamics is important both in the study of mechanics and in engineering, where forces must be considered in design and function. Several forces, such as drag and thrust, act on objects. To move, an object must overcome various forces, including frictional forces and inertia.

Background

The works of Galileo Galilei and Sir Isaac Newton are integral to understanding physics. They were not the first to study physics and develop theories about dynamics, but they studied earlier observations and theories and tested old ideas based on new discoveries. The works of ancient Greek philosophers, such as Aristotle, formed the basis of much scientific research.

Galileo made his own crude telescope based on descriptions of a new invention in 1609. His observations led to an early understanding of dynamics. He discovered sunspots and realized that the Sun was rotating, which meant Earth might also rotate. He discovered four moons around Jupiter. This discovery lent further weight to the idea that the planets orbit the Sun, because many believed that if Earth was in orbit around the Sun, the Moon would be left behind. Yet, something held the moons of Jupiter in orbit. With his telescope, Galileo proved the heliocentric model of the universe.

Galileo is credited with the Leaning Tower of Pisa experiment, which involved dropping two objects of different weights from the tower, though it is likely he did not conduct this experiment himself. He did conduct a series of experiments using inclined planes, which helped him study the effects of gravity on objects. He showed that the acceleration of falling objects of very different weights is due to gravity rather than the weight of the object. He developed the concept of inertia, which is an object's resistance to a change in its state of motion. Galileo corrected Aristotle's ideas about motion—objects at rest remained at rest unless a force acted on them, but objects in motion did not continue to move unless a force continued to act on them. Galileo realized that Aristotle had not considered the frictional force between the moving object and the surface on which it traveled. The frictional force opposes the force that pushes an object. Any change in the frictional force—such as oiling the surface—changes the effects of the force of movement. Galileo's law of inertia states that if frictional forces could be eliminated, an object pushed at constant speed on an infinite frictionless surface would continue moving at the same speed forever, even if the motion force ceases, unless another force acts on it. Although frictional forces cannot be eliminated, they can be reduced to near zero.

Newton was born in 1643, the year after Galileo's death. He studied mathematics and physics, and in 1666 developed the theories of gravitation. He later developed his three laws of motion:

• Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.
• Force is equal to the change of momentum (mV) per change in time. For a constant mass, force equals mass times acceleration: F=ma.
• For every action, there is an equal and opposite reaction, or the mutual actions of any two bodies are always equal and oppositely directed.

The first law is essentially the definition of inertia. An object on which no net force is acting will maintain a constant velocity, which is zero if it is not moving. Examples include a ball falling through the atmosphere or the movement of a kite due to a change in the wind. The second law explains how an external force changes an object's velocity. The change of velocity is determined by the object's mass. According to the third law, when one object exerts force on another, it is subject to an equal force exerted by the second object.

Overview

The general principles of dynamics are based on the laws of motion, which have an impact on the design and operation of machines. Many of the issues to be considered are action-at-a-distance forces, including gravitational force, electrical force, and magnetic force, and contact forces, which include frictional force, applied force, and air resistance. An applied force is a force applied to an object; it can be applied by another object or, for example, a person. Gravity force (weight) is applied by a large object, such as a planet or moon. Normal force is the support force a stable object exerts on another object. (The surface of a desk, for example, exerts upward force on items resting on it.) Air resistance acts on an object traveling through the air and usually acts against the object's motion. Tension force is the force in a cable, rope, string, or wire when forces on opposite ends are applied, pulling it tight. Spring force is force on an object attached to a spring that is compressed or stretched.

Aircraft and spacecraft designers and operators must consider the dynamics of flight and a number of forces. Four forces of flight that must be addressed are lift, drag, weight, and thrust.

Planes fly because their wings are designed to affect the air as it moves over the wing. The wings make the air over the top move faster, which decreases the pressure of the air. This creates lift, or an upward force. Drag is a backward force on an airplane. Weight is a downward force, and thrust is a forward force. Other forces, such as frictional force, may be reduced, such as by the use of wheels on the ground.

A plane's wings have flaps, called ailerons, on the back edge. The pilot can raise and lower the ailerons. This affects the lift on the wings by changing the resistance on the wings. When the pilot raises the aileron on one wing and lowers it on the other, the plane rolls so the side with the raised aileron goes down and the side with the lowered aileron goes up.

Bibliography

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"Laws of Motion: Galileo and Newton." New Mexico State University, astronomy.nmsu.edu/aklypin/WebSite/NewtonI.pdf. Accessed 30 Jan. 2017.

"Newton's Laws, Vectors, and Reference Frames." Massachusetts Institute of Technology Open Courseware, https://ocw.mit.edu/courses/mechanical-engineering/2-003sc-engineering-dynamics-fall-2011/newton2019s-laws-vectors-and-reference-frames/. Accessed 30 Jan. 2017.

"Nova: Galileo's Inclined Plane." PBS Learning Media, pbslearningmedia.org/resource/phy03.sci.phys.mfw.galileoplane/galileos-inclined-plane/. Accessed 30 Jan. 2017.

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"Types of Forces." The Physics Classroom, www.physicsclassroom.com/class/newtlaws/Lesson-2/Types-of-Forces. Accessed 30 Jan. 2017.