Newton knew that the force which caused the apple's acceleration (gravity)
must be dependent upon the mass of the apple. And since the force acting
to cause the apple's downward acceleration also causes the earth's upward
acceleration (Newton's third law), that force must also depend upon the mass
of the earth. So for Newton, the force of gravity acting between the earth
and any other object is directly proportional to the mass of the earth, directly
proportional to the mass of the object, and inversely proportional to the
square of the distance which separates the centers of the earth and the object.
We have seen that in the Universal Law of Gravitation the crucial quantity is
mass. In popular language mass and weight are often used to mean the same
thing; in reality they are related but quite different things. What we
commonly call weight is really just the
gravitational force
exerted on an
object of a certain mass. We can illustrate by choosing
the Earth as one of the two masses
in the previous illustration of the Law of Gravitation:
The proportionalities expressed by Newton's universal law of gravitation is
represented graphically by the following illustration. Observe how the force
of gravity is directly proportional to the product of the two masses and inversely
proportional to the square of the distance of separation.
The Bellman equation is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming in various scientific fields.
RDF/XML allows further abbreviating RDF URI references in XML attributes in two
ways. The XML Infoset provides a base URI attribute xml:base
that sets the base URI for resolving relative RDF URI references, otherwise the base URI is that of the document. The base URI applies to
all RDF/XML attributes that deal with RDF URI references which are rdf:about,
rdf:resource, rdf:ID
and rdf:datatype.
01
of 16
Surface Area and Volume of a Sphere
D. Russell
Surface Area = 4πr2
Volume = 4/3 πr3
A three-dimensional circle is known as a sphere. In order to calculate either the surface area or the volume of a sphere, you need to know the radius (r). The radius is the distance from the center of the sphere to the edge and it is always the same, no matter which points on the sphere's edge you measure from.
Once you have the radius, the formulas are rather simple to remember. Just as with the circumference of the circle, you will need to use pi (π). Generally, you can round this infinite number to 3.14 or 3.14159 (the accepted fraction is 22/7).
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