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# Lect_06 - Lecture 6 Circular Motion A battleship...

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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 2 t A in the air, where t A is the time it takes for v y to become zero: 0 = v 0A y — gt A . v 0A y > v 0B y 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 π radians 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 ω = = Radial velocity Angular velocity (where ω is in radians/unit time) ds d s R R v R dt dt θ θ ω = → = → = v r = 0 For circular motion: EXAMPLE: Two balls EXAMPLE: Two balls Two balls connected by thin rod as shown, at distances R and 2 R from the center, move in circles....
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Lect_06 - Lecture 6 Circular Motion A battleship...

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