PHYS_2014_Lecture_7

PHYS_2014_Lecture_7 - Fall 2010 Oklahoma State University...

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Unformatted text preview: Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 7, Slide 1 r v I swing a ball attached to a string of length r over my head. The path that the ball takes is a circle of radius with my hand at the origin. At any given instant, the velocity, , of the ball is a vector tangent to the circular path, i.e. . a v a r a a v r Lecture 7: Circular Motion Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 7, Slide 2 Circular or rotational motion , while common in everyday life, is different from the linear motion we have studied so far. Circular motion is clearly different from the straight-line motion of objects sliding or rolling over surfaces (inclined or otherwise) and is clearly different from projectile motion wherein objects follow parabolic trajectories. One difference is that circular motion repeats...the object traverses the same path, i.e. the same circular trajectory, over and over again. r v Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 7, Slide 3 Because the motion is constrained to a circle, we can specify all possible positions where the object (ball) might be in terms of the radius, , and the angle, . Thus, it makes sense to use a polar coordinate system. 2 2 1 cos sin tan = = = + = a a x r i y r j r x y y x r y x a r Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 7, Slide 4 r s x The distance traveled by an object undergoing circular motion can be found by the radius r and the change in the angle . (radians) s r = (radians) s r = s is not in a straightline . It is the segment of the circumference of a circle and is referred to as arc length. Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 7, Slide 5 The length of one circular path around my hand is the circumference of the circle of radius r . If the ball Im swinging above my head takes a time T (the period) to complete one circular path, the the balls speed will be: 2 s r = 2 s r v t T = = r v Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 7, Slide 6 We can apply this to the Earths motion around the Sun. The average distance between the Sun and the Earth is 1.49 10 11 m and the time it takes the Earth to go around (orbit) the Sun one time is 365.25 days or 3.16 10 7 s. 11 4 7 2 1.49 10 m 2.91 10 m s 65,000miles hr 3.16 10 s v = = Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 7, Slide 7 Consider our original definitions for velocity and acceleration and s v v a t t = = a a a a As defined here, position, velocity, and acceleration are all vectors. By definition a vector has both magnitude and direction....
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This note was uploaded on 11/28/2011 for the course PSYCH 2014 taught by Professor Staff during the Fall '10 term at Oklahoma State.

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PHYS_2014_Lecture_7 - Fall 2010 Oklahoma State University...

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