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Chapter%205

# Chapter%205 - COLLEGE PHYSICS Part I Chapter 5 Dynamics of...

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COLLEGE PHYSICS, Part I Chapter 5: Dynamics of Uniform Circular Motion Uniform Circular Motion Centripetal Acceleration Centripetal Force Banked Curves Satellite Motion Apparent Weightlessness Vertical Circular Motion

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Uniform Circular Motion Uniform circular motion is when a particle moves in a circle with constant speed. For uniform circular motion (see the right panel), the acceleration is perpendicular to the velocity; it maintains its magnitude but changes its direction as the velocity changes its direction. The acceleration vector at each point of the circular path is directed toward the center of the circle, i.e., is colinear with the radius of the circle. Therefore, it is called radial acceleration, or centripetal acceleration.
1 v s v R = r 1 v v s R = r 1 av v v s a t R t = = r 1 1 0 0 lim lim t t v s v s a R t R t ∆ → ∆ → = = 1 0 lim t s v t ∆ → = 2 rad v a R = The two triangles shown in panels a and b are similar because they both are isosceles triangles and have the same angle ∆φ . or By definition, for the average acceleration we have: For the instantaneous acceleration we have: But, Hence, Hence,

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Because the acceleration of an object in uniform circular motion is always directed toward the center of the circle, it is often called a centripetal acceleration.
R = 5 m Time of a complete circle (the period) T = 4 s A Carnival Ride Find the acceleration 7.85m/s T R 2 v = = π ( 29 2 2 2 12.3m/s 5m 7.85m/s R v a = = =

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Centripetal Force 2 rad v a R = Consider motion along a circle, with constant speed. The acceleration is constant in magnitude, and is directed toward the center of the circle. It is called radial, or centripetal acceleration. The radial acceleration can also be expressed in terms of the period T , the time per one revolution 2 R v T π = 2 2 4 rad R a T π = Since ,
According to Newton’s second law, if there is constant acceleration, there is a constant force directed to the same direction. From this we have: In this example, F rad is the tension in the string that pulls the ball constantly to the center. The force related to the centripetal acceleration is known as the centripetal force . Example: You fly a propeller-driven airplane on a 5.00 m string in a horizontal circle.

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