Physics 111: Elementary Mechanics – Lecture 12

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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. Center for Solar-Terrestrial Research

9. Potential and Kinetic Energy Potential Energy Kinetic Energy Total Energy Center for Solar-Terrestrial Research

10. Einstein and Gravitation Center for Solar-Terrestrial Research