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Physics 101: Lecture 11 Centripetal Force z z Brief Review of Chapters 1-4 Textbook Chapter 5 ÎUniform circular motion : satellites in circular orbits, apparent weightlessness and artificial gravity Physics 101: Lecture 11, Pg 1 Centripetal Force Centripetal acceleration: ac v2 = R Acceleration is the result of a net-force acting on an object. In case of ac this net-force is called centripetal force, Fc: Magnitude of Fc: Fc= Σ F= m ac= m v2/R Direction of Fc: always points towards the center of the circle Define frequency f, period T, angular velocity ω: ac = (2π f ) R 2 2 2π ac = R T ac = ω 2 R The period T is the time required to travel once around the circle, ie to make one complete revolution: T=2π R/v Physics 101: Lecture 11, Pg 2 Satellites in Circular Orbits Satellites in circular orbits are examples of uniform circular motion. What provides the centripetal force ? The gravitational pull of the earth: Fc= G M m/r2 = mv2/r z ⇒ 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 3 Synchronous Satellites z 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 104 s = 2π r/v and v=(G M/r)1/2 ⇒ r3/2=T (GM)1/2/(2π) => r=4 x 107 m ⇒ H=r-rE=3.6 x 107 m = 22300 miles Physics 101: Lecture 11, Pg 4 Circular Motion: More Examples 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. z 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. z Physics 101: Lecture 11, Pg 5