JumpStart - Physical Science
Newton's Laws of Motion - Does It Matter?*

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Three Distinct Laws of Motion

The motion of objects can be explained and described by physical principals discovered over three hundred years ago by Sir Isaac Newton. Newton worked in many areas of mathematics and physics. He developed the theories of gravitation in 1666, when he was only 23 years old. Some twenty years later, in 1686, he presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis". Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. The key point here is that if there is no net force acting on an object, or if all the external forces cancel each other out, then the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest. If an external force is applied, the velocity will change because of the force.

The second law explains how the velocity will change. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. Newton also developed the calculus of mathematics, and the "changes" expressed in the second law are accurately defined in differential forms. (Calculus can also be used to determine the velocity variation and the location variation experienced by an object subjected to an external force.) For an object with a constant mass, the second law can be more easily expressed as the product of an object's mass and it's acceleration (F = ma). For an external applied force, the change in velocity depends on the mass of the object. A force will cause a change in velocity; and likewise, a change in velocity will generate a force. The equation works both ways.

The third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal force on object A. Notice that the forces are exerted on different objects. The third law can be used to explain the generation of lift lift by a wing and the production of thrust thrust by a jet engine.

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First Law
Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. The key point here is that if there is no net force acting on an object (if all the external forces cancel each other out) then the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest. And if an additional external force is applied, the velocity will change because of the force.

An object falling through the atmosphere is a good example of this principle. Just prior to release, the velocity of the object is zero, the object is at rest, and the weight of the object is balanced by some restraining device (a rope). There is no net force on the object, and the object would remain at rest indefinitely. When the rope is cut, the object is subjected to a single force, the gravitational attraction of the earth. Since there is no initial air resistance, the object begins to free fall and accelerate. But as the object velocity increases, it encounters air resistance, or drag, which opposes the motion. The magnitude of the drag depends on the square of the velocity. The drag increases until it is equal to the weight. At that point, there is no net external force on the object, the acceleration goes to zero, and the body falls at a constant terminal velocity. The magnitude of the velocity depends on the relative magnitude of the weight, the drag coefficient, the air density, and the size of the object.

Second Law
His second law defines a force to be equal to the differential change in momentum per unit time as described by the calculus of mathematics which Newton also developed. The momentum is defined to be the mass of an object times its velocity. If the mass is a constant, the second law reduces to the more familiar product of a mass and an acceleration (F = ma). Since acceleration is a change in velocity with a change in time, we can also write this equation in the third form shown on the slide. The important fact is that a force will cause a change in velocity; and likewise, a change in velocity will generate a force. The equation works both ways. The velocity, force, acceleration, and momentum have both a magnitude and a direction associated with them. Scientists and mathematicians call this a vector quantity (magnitude plus direction.)

The motion of an aircraft resulting from aerodynamic forces and the aircraft weight and thrust can be computed by using the second law of motion.

In this demonstration, a simple model of a satellite orbiting Earth is created from a large stationary ball and a smaller ball at the end of a string. The ball and string become a pendulum that tries to swing toward the middle of the globe. However, the ball travels in an orbit around the globe when it is given a horizontal velocity in the correct direction. Although the small ball attempts to fall to the center of the larger ball, its falling path becomes circular because of its horizontal velocity Adapted from NASA's "A Teacher's Guide With Activities", produced by the Microgravity Science and Applications Division, Office of Space Science and Applications, and NASA's Education Division, Office of Human Resources and Education.

http://wwwssl.msfc.nasa.gov/msl1/ground_lab/aroundtheworld.htm

Third Law
His third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A. Notice that the forces are exerted on different objects.

For aircraft, the principal of action and reaction is very important. It helps to explain the generation of lift from an airfoil. In this problem, the air is deflected downward by the action of the airfoil, and in reaction the wing is pushed upward. Similarly, for a spinning ball, the air is deflected to one side, and the ball reacts by moving in the opposite direction. A jet engine also produces thrust through action and reaction. The engine produces hot exhaust gases which flow out the back of the engine. In reaction, a thrusting force is produced in the opposite direction.

Material prepared by Tom Benson (benson@grc.nasa.gov), a research scientist in the Turbomachinery and Propulsion Systems Division, NASA Glenn Research Center, edited by Ruth Petersen (Ruth.A.Petersen@grc.nasa.gov), Integral Systems, Inc.; Susan Martin-Vorndran, RSIS; and Roger Storm, Science Department Chairman at Fairview Park High School and one of the original authors of FoilSim.

URL: http://www.grc.nasa.gov/WWW/K-12/airplane/short.html