Centripetal Motion Galileo ( ) 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

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

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

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

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

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!

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?

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

A different Normal Force y x y NxNx mg acac