Physics 101: Lecture 11, Pg 1 Physics 101: Lecture 11 Centripetal Force l Brief Review of Chapters 1-4 l Textbook Chapter 5 è Uniform circular motion : satellites in circular orbits, apparent weightlessness and artificial gravity

Physics 101: Lecture 11, Pg 2 Centripetal Force Define frequency f, period T, angular velocity  : Centripetal acceleration: Acceleration is the result of a net-force acting on an object. In case of a c this net-force is called centripetal force, F c : Magnitude of F c : F c =  F= m a c = m v 2 /R Direction of F c : always points towards the center of the circle The period T is the time required to travel once around the circle, ie to make one complete revolution: T=2  R/v

Physics 101: Lecture 11, Pg 3 Satellites in Circular Orbits l Satellites in circular orbits are examples of uniform circular motion. What provides the centripetal force ? The gravitational pull of the earth: F c = G M m/r 2 = mv 2 /r  Orbital speed of statellite : v = (GM/r) 1/2 => v does not depend on mass of satellite ! Synchronous satellites: Orbital period T=1 day = time it takes for the earth to turn once around its axis. => Satellite always appears to be at a fixed position in the sky -> stationary relay stations for communication signals sent up from earth.

Physics 101: Lecture 11, Pg 4 Synchronous Satellites l To serve as stationary relay station the satellite must be placed at a certain height above the earth surface: T=1 day=8.64 x 10 4 s = 2  r/v and v=(G M/r) 1/2  r 3/2 =T (GM) 1/2 /(2  ) => r=4 x 10 7 m  H=r-r E =3.6 x 10 7 m = miles

Physics 101: Lecture 11, Pg 5 Circular Motion: More Examples l Apparent weightlessness: Apparent weight in a satellite is zero just as in a free falling elevator : Person and scale fall with the same acceleration towards the center of earth => they cannot push against each other. l Artificial gravity: In a rotating space laboratory a push on a persons feet equal to mg can be simulated by the centripetal force if v = (r g) 1/2.