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Centripetal Motion Galileo (1564-1642) already demonstrated to us ( chapter 3) that the magnitude of the centripetal acceleration is given by: He deduced this from the law of falling bodiesa method Newton later perfected: s h v v R L

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Newton generalized! In a circular orbit, F pulls the object inward, v = 2 R/T

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Some special cases Object moving in a horizontal circle The only force acting is the tension, so T = mv 2 /r What happens if you pull harder? V increases! V TTop view r

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How about a vertical circle? Will the tension be greater or less at the bottom? How about the velocity? mg v T mg v

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Buy Low and Sell High? Should you buy gold at the equator and sell it near the pole, or vice versa?

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So why is Saturn so Squished? Saturns oblateness is 11% Saturns oblateness is 11% (Equator – R pole )/R equator =.11 (Equator – R pole )/R equator =.11 Rotation Rate is 9 hrs (.375T E ) Rotation Rate is 9 hrs (.375T E ) Orbital radius is 9R E Orbital radius is 9R E a c =.034*(9/.375 2) =2.2m/s 2 a c =.034*(9/.375 2) =2.2m/s 2 Centripetal Force due to gravity not sufficient to hold gas into Polar Radius! Centripetal Force due to gravity not sufficient to hold gas into Polar Radius!

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A different Normal Force What direction is the normal force on this car due to the banked track? What direction is the centripetal acceleration? What direction is gravity pointing?

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A different Normal Force Lets fill in the details..x and y coordinates Resolve Normal force into components Write down Force equations in x and y dir. y x y NxNx mg acac

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A different Normal Force y x y NxNx mg acac

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Dynamics of Uniform Circular Motion

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