I.
Momentum = mv, where m = inertial mass of the body,
v = velocity of the body
II.
Newton's Laws of Motion:
A.
Every body persists in its state of rest or of uniform motion in a straight
line, except or until that state is changed by some impressed force.
B.
The force acting on a body is numerically equal to the rate of change of
momentum of the body, and the rate of change of momentum is in the direction
of the applied force.
F
= rate of change of (mv)
or,
F=ma when the mass, m, remains constant
C. To
every action (some force exerted on body A by body B) there is an equal
and opposite reaction (force exerted by body A on body B).
III.
Uniform circular motion:
IV.
Newton's Law of Universal Gravitation:
Newton
eventually had the following information:
A.
Kepler's laws of planetary motion:
1.
Elliptical orbits, with the sun at one focus.
2.
Equal areas in equal times.
3.
For all planets,
where
p = planet's period about the sun, R = average distance of planet from
sun, k = a constant.
B. The
law of free fall
where
D = distance, T = time of fall, A = acceleration due to gravity.
C. Newton's
three laws of motion:
1.
Law of Inertia.
2.
Law of relation between force, mass, and acceleration: F = ma.
3.
Law of action and reaction.
D. Law
of force necessary to keep a body moving uniformly in a circle:
V.
Newton assumed:
A.
That the laws of motion hold everywhere in the universe;
B.
(initially) that the orbits of the planets were circular rather than elliptical.
The
result:
Newton's
Law of Universal Gravitation: Every body in the universe attracts every
other body with a force directly proportional to the Foduct of their masses
and inversely proportional to the square of the distance between them.
As
a formula, this law is expressed as follows:
Force
is equal to the Gravitational Constant times: Mass one time Mass
two, divided by the radius (distance) squared.
Where
F = the force of attraction, m and M = the two masses, R = the distance
between the two masses, and G = the universal constant of gravitation.
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