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Computer Drawing of an airliner with the math equations
 for Newton's Second Law of Motion

 

Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. 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 form that force (F) is equal to the mass (m) times the acceleration (a) :

F = m * a

Since acceleration is a change in velocity (V) with a change in time (t), we can also write this equation in the difference form shown on the slide.

F = m * (V1 - V0) / (t1 - t0)

The important fact is that a force causes a change in velocity; and likewise, a change in velocity generates 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 equations shown here are actually vector equations and can be applied in each of the component directions.

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


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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Jun 12 2014

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