Study Guide -- Gravity (Mr. Rogers AP Physics C )

 Unit Plan Practice Test Study Guide
 Mathematical Models
 Universal Gravity Force F = (G∙M∙m) / r2 Simple x = (xmax) cos (ωt) Gravity Field g = (G∙M) / r2 Harmonic v = -ω (xmax) sin (ωt) Motion a = -ω2 (xmax) cos (ωt) Gravitational Potential Energy Ur = - m [G(M) / r] Air Resistance F = Bv Centripetal Accel. a = m v2 / r Terminal Velocity vterminal = mg / B Circular Orbit Velocity v = [(GM) / r]^0.5 V vs. time v = (mg / B) ( 1 - e - (b/m) t ) Escape Velocity v = [(2GM) / r]^0.5
 Key Principles
 Standard for gravitational potential energy: When deriving or calculating the gravitational potential energy around a planet, infinity is assumed to be zero potential energy. Hence, any distance less than infinity will have a negative potential energy.
 Problem Solving Tips: Rotation
 Example Problems
 Derivation of the time to fall through a tunnel through the center of the Earth Derivation of escape velocity Derivation of gravitational potential energy equation Find g on a different planet: the planet Zorg has twice as much mass and is half as big in diameter as Earth. Find g on Zorg. Derivation of circular orbit velocity

 Vocabulary
 force field escape velocity terminal velocity air resistance
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