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Unformatted text preview: Lecture 6 Circular Motion A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first? A. A B. B C. Both at the same time ACT: Battleship The vertical part of the motion dictates the time a projectile spends in the air. t A t A Shell A spends 2t A in the air, where t A is the time it takes for v y to become zero: 0 = v 0Ay — gt A . v 0Ay > v 0By because A goes higher. Thus, t A > t B Circular Motion Circular Motion Circular motion is the motion in a circle with constant radius. Relation to Cartesian coordinates: x = r cos θ y = r sin θ Polar coordinates Polar coordinates (r, θ ) are more convenient than Cartesian coordinates to describe circular motion: r = R, only θ = θ (t) Arch: s = R θ Definition: 1 radian = angle so that s=R 1 revolution = 2 radians π θ y x s R Velocity Velocity Cartesian coordinates: ; x y dy dx v v dt dt = = Polar coordinates: ; r dr d v dt dt θ ϖ = = Radial velocity Angular velocity (where ϖ is in radians/unit time) ds d s R R v R dt dt θ θ ϖ = = = v r = 0 For circular motion: EXAMPLE: Two balls EXAMPLE: Two balls Two balls connected by thin rod as shown, at distances R and 2R from the center, move in circles....
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 Fall '08
 HerreraSiklody
 Circular Motion, Trigraph, Polar coordinate system, acce ration, Magnitudeof Radial Acce

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