Circular motion and gravitation formula sheet, Cheat Sheet of Physics

Download Circular motion and gravitation formula sheet and more Cheat Sheet Physics in PDF only on Docsity! Circular Motion and Gravitation Summary Sheet Chapter 5 Horizontal Circle: Mass on String ΣFc = mac FT = mac r m FT Newton’s Law of Universal Gravitation “Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles.” Equation Resulting from Law of Universal Gravitation 2 21 G r mm GF = G = 6.67 x 10-11 Nm2/kg2 r is the center to center distance. m1 m2 FG FG r Planetary Motion – Kepler’s Laws 1st law: “The path of each planet about the Sun is an ellipse with the Sun at one focus.” 2nd law: “Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time.” 3rd law: The ratio of the squares of the periods (the time needed for one revolution about the Sun) of any two planets revolving about the Sun is equal to the ratio of the cubes of their mean distances from the Sun. Or in equation form: 3 2 1 2 2 1 r r T T !! " # $$ % & =!! " # $$ % & Note: use this equation to compare two objects that orbit the same mass. Examples: two planets that orbit the Sun; moons or satellites that orbit the same planet. Vertical Circle: Mass on String Top ΣFc = mac F + mg = mac Bottom ΣFc = mac F - mg = mac r m F mg m F mg Circular Motion Equations Period completed circles of # timeelapsed T = units: seconds Frequency timeelapsed completed circles of # f = units: 1/second or Hz Tangential Speed T r !2 v = units: m/s Centripetal Acceleration r v a 2 c = units: m/s2 FN mg ΣFc = mac -FN + mg = mac If the car looses contact with road, FN = 0. FN mg ΣFc = mac FN - mg = mac Vertical Circle: Car on Road FN mg FS ΣFc = mac FS = mac µsFN = mac Horizontal Circle: Car on Track FN mg ΣFc = mac FN + mg = mac Vertical Circle: Inverted Roller Coaster Cars Other Useful Equations Derived in Class Acceleration due to gravity above any planet or moon: 2c r M Ga = To find the mass of the object being orbited: 2 32 T r G !4 M = Speed of mass in orbit: r M Gv = M m r v ac ΣFc = mac FG = mmac cm2 mE am r mm G = c2 E a r m G = Horizontal Circle: Moon Orbits Earth mE mm r