Physics 111: Elementary Mechanics – Lecture 12

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# Physics 111: Elementary Mechanics Lecture 12 - PowerPoint PPT Presentation

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

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.
• Static equilibrium: and
• Stable and unstable static equilibrium

Center for Solar-Terrestrial Research

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

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

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

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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

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.

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Potential and Kinetic Energy

Potential Energy

Kinetic Energy

Total Energy

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Einstein and Gravitation

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