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Unformatted text preview: PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 12 • Newton’s Law of gravitation • Kepler’s Laws of Planetary motion 1. Ellipses with sun at focus 2. Sweep out equal areas in equal times 3. Last Lecture F grav = GMm R 2 G = 6.67 " 10 # 11 Nm 2 / kg 2 R 3 T 2 = GM 4 " 2 = Constant • PE = mgh valid only near Earth’s surface • For arbitrary altitude • Zero reference level is at r= ! PE = ! G Mm r Gravitational Potential Energy Example 7.18 You wish to hurl a projectile from the surface of the Earth (R e = 6.38x10 6 m) to an altitude of 20x10 6 m above the surface of the Earth. Ignore rotation of the Earth and air resistance. a) What initial velocity is required? b) What velocity would be required in order for the projectile to reach infinitely high? I.e., what is the escape velocity? c) (skip) How does the escape velocity compare to the velocity required for a low earth orbit? a) 9,736 m/s b) 11,181 m/s c) 7,906 m/s Chapter 8 Rotational Equilibrium and Rotational Dynamics Wrench Demo Torque • Torque, " , is tendency of a force to rotate object about some axis • F is the force • d is the lever arm (or moment arm) • Units are Newtonmeters !...
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This note was uploaded on 07/25/2008 for the course PHY 231 taught by Professor Smith during the Spring '08 term at Michigan State University.
 Spring '08
 smith
 Physics

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