Physics 111 elementary mechanics lecture 12
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Physics 111: Elementary Mechanics – Lecture 12. Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research. 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.

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Physics 111 elementary mechanics lecture 12 l.jpg

Physics 111: Elementary Mechanics – Lecture 12

Carsten Denker

NJIT Physics Department

Center for Solar–Terrestrial Research


Equilibrium l.jpg
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

Center for Solar-Terrestrial Research


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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

Center for Solar-Terrestrial Research


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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 body’s center of gravity is coincident with the body’s center of mass.

Center for Solar-Terrestrial Research


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Newton’s Law of Gravitation

A uniform spherical shell shell of matter attracts a particles that is outside the shell as if all the shell’s mass is concentrated at its center!

G = 6.67  10–11 N m2/kg2

Superposition Principle

Center for Solar-Terrestrial Research


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Gravitation Near Earth’s 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)

Center for Solar-Terrestrial Research


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Kepler’s 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 planet’s 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.

Center for Solar-Terrestrial Research



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Potential and Kinetic Energy

Potential Energy

Kinetic Energy

Total Energy

Center for Solar-Terrestrial Research


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Einstein and Gravitation

Center for Solar-Terrestrial Research