Physics 111: Elementary Mechanics Lecture 12

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Physics 111 Elementary Mechanics Lecture 12

• Carsten Denker
• NJIT Physics Department
• Center for SolarTerrestrial Research

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Equilibrium

• The linear momentum P of the center of mass is
  constant.
• The angular momentum L about the center of mass,
  or about any other point, is constant.
• Static equilibrium and
• Stable and unstable static equilibrium

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Requirement of Equilibrium

• The vector sum of all external forces that act on
  a body must be zero.
• The vector sum of all external torques that act
  on a body, measured about any possible point,
  must also be zero.
• The linear momentum of the body must be zero.

balance of forces
balance of torques
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Center of Gravity

• The gravitational force on a body
  effectively acts on a single point, called the
  center of gravity.
• If is the same for all elements of a body,
  then the bodys center of gravity is coincident
  with the bodys center of mass.

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Newtons Law of Gravitation
A uniform spherical shell shell of matter
attracts a particles that is outside the shell as
if all the shells mass is concentrated at its
center!
G 6.67 ? 1011 N m2/kg2 Superposition Principle
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Gravitation Near Earths Surface
Gravitational acceleration

• Earth is not uniform
• Earth is not a sphere
• Earth is rotating

Mean Earth surface (0 km, 9.83 m/s2), Mt. Everest
(8.8 km, 9.80 m/s2), highest manned balloon (
36.6 km, 9.71 m/s2), Space Shuttle orbit (400 km,
8.70 m/s2), and communications satellite (35,700
km, 0.225 m/s2)
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Keplers Laws

• The Law of Orbits All planets move in elliptical
  orbits, with the Sun at one focus.
• The Law of Areas A line that connects the planet
  to the Sun sweeps out equal areas in the plane of
  the planets orbit in equal times, i.e., the rate
  dA/dt at which it sweeps out area A is constant.
• The Law of Periods The square of the period is
  proportional to the cube of the semimajor axis of
  its orbit.

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Potential and Kinetic Energy
Potential Energy
Kinetic Energy
Total Energy
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Einstein and Gravitation