UNIFORM CIRCULAR MOTION AND GRAVITATION

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UNIFORM CIRCULAR MOTION AND GRAVITATION
Uniform Circular Motion Centripetal Force
Gravitation Keplers Laws Gravitational
Potential Energy
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Any object traveling in a circular path, or
section of a circular path, is in circular
motion. If the objects speed is constant during
this motion, the motion is called uniform
circular motion. EXAMPLES A ball being swung in
a horizontal, circular path at the end of a
string A car going around a turn A roller coaster
car going over a hill or loop, or around a
turn An airplane in a turn or loop A satellite in
orbit
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GRAVITATIONAL POTENTIAL ENERGY Previously, we
studied gravitational potential energy for
objects near the earths surface and not
experiencing large changes in elevation. In such
cases, the free-fall acceleration, g, is very
nearly constant and was treated as so. We used PE
mgh for an objects potential energy where h
was measured from an arbitrary reference. Now we
are going to consider objects moving over great
distances and not close to the surface distances
over which the value of g changes significantly.
In such cases, an objects potential energy is
set to zero when it is infinitely far from earth.
As the object approaches earth, its potential
energy is negative and decreases the closer it
gets. The equation used for gravitational
potential energy for an object of mass mobject in
this case is
r is measured form the center of the earth.
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EXAMPLE Calculate the escape velocity from the
earth for an object at rest on its surface. The
escape velocity is the minimum speed needed by an
object to escape the gravitational influence of
earth without ever falling back or needing
additional thrust.
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ANSWER Calculate the escape velocity from the
earth for an object at rest on its surface. The
escape velocity is the minimum speed needed by an
object to escape the gravitational influence of
earth without ever falling back or needing
additional thrust.