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 m times its velocity
v. So the differential equation for force F is:
F = d(m * v) / dt
If the mass is a constant and using the definition of acceleration a as the
change in velocity with time, the second law reduces to the more familiar product
of a mass and an acceleration:
F = m * a
Since acceleration is
a change in velocity with a change in time t, we can also write this equation
in the third form shown on the slide:
F = m * (v1  v0) / (t1  t0)
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.
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
aerodynamic forces and the aircraft
weight and thrust
can be computed by using the second law of motion.
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