Lecture214Week4

Lecture214Week4 - Circular Motion Circular motion is very...

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05/07/09 Physics 214 Fall 2008 1 Circular Motion Circular motion is very common and very important in our everyday life. Satellites, the moon, the solar system and stars in galaxies all rotate in “circular” orbits. The term circular here is being used loosely since even repetitive closed motion is generally not a perfect circle. At any given instant an object that is not moving in a straight line is moving along the arc of a circle. So if we understand motion in a circle we can understand more complicated trajectories. Remember at any instant the velocity is along the path of motion but the acceleration can be in any direction .
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05/07/09 Physics 214 Fall 2008 2 Circular motion If the velocity of an object changes direction then the object experiences an acceleration and a force is required. This is centripetal acceleration and force and is directed toward the center of the circle. This is the effect you feel rounding a corner in a car
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05/07/09 Physics 214 Fall 2008 3 Balance of forces We need to understand the forces that are acting horizontally and vertically. In the case shown the tension or force exerted by the string has components which balance the weight in the vertical direction and provide the centripetal force horizontally.
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05/07/09 Physics 214 Fall 2008 4 Cars When a car turns a corner it is friction between the tires and the road which provides the centripetal force. If the road is banked then the normal force also provides a force. For a banked track there is a velocity for which no friction is required. F f Above W = mg F f F f Rear
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05/07/09 Physics 214 Fall 2008 5 Vertical circles If v = 0 then N = mg As v increases N becomes smaller Ferris wheel g At the bottom + is always toward the center of the circle W = mg N v
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05/07/09 Physics 214 Fall 2008 6 Gravitation and the planets Astronomy began as soon as man was able to observe the sky and records exist going back several thousand years. In particular the yearly variation of the stars in the sky and the motion of observable objects such as planets. People observed the “fixed” North Star and, for example, the rising of Sirius signalling the flooding of the Nile. Copernicus was the first person to advocate a sun centered solar system. Followed by Galileo who used the first telescopes Tycho Brahe was the most famous naked eye astronomer. Kepler, his assistant used the data to draw quantitative conclusions.
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05/07/09 Physics 214 Fall 2008 7 Keplers Laws 1) Orbits are ellipses 2) The radius vector sweeps out areas in equal times equal 3) T 2 proportional to r 3 T is the period which for the earth is one year and r is the average radius For circular motion with constant velocity v The circumference of a circle is 2πR and the Period T = 2πr/v
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Physics 214 Fall 2008 8 Newton and Gravitation Newton developed the Law of Gravitation force between two objects is F = GM 1 m 2 /r 2 . The constant of
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This note was uploaded on 05/03/2009 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture214Week4 - Circular Motion Circular motion is very...

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