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Published byDaniella Day Modified over 9 years ago
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Jump to first page 1 Chapter 3 Kinematics of particles Differentiation: the ratio between two increments when they are extremely small, e.g. velocity. Increment: distance traveled at the end of the 1 st second = 10 m distance traveled at the end of the 3 rd second = 14 m increment of distance = 4 m increment of time = 2 s Ratio between two increments = 4 m/2s = 2 m/s (average velocity) More detailed measurement: distance traveled at the end of 1.01 second, the distance traveled is 10.025 m, the ratio becomes 0.025 m / 0.01 s = 2.5 m/s (instantaneous velocity).
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4 y x z O Instantaneous velocity Acceleration Position
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Jump to first page 5 Cartesian coordinate system x z y
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Jump to first page 6 2D Polar coordination system y x O : unit vector // to (radial) : unit vector to (in -direction)
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Jump to first page 7 Velocity Since radial velocity tangential velocity angular velocity O x y
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Jump to first page 8 centripetal acceleration. Acceleration Since
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Solution
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Jump to first page 11 0.08m 0.04m P A O r Solution For OAP, 0.08 2 = 0.04 2 +r 2 +2 x 0.04 r cos Time derivative: At = 90 o, r = 0.06928 m
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Jump to first page 12 3D Cylindrical coordination system x z y z r
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Jump to first page 13 Normal and Tangential Coordinates (n-t) : radius of curvature O’
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Jump to first page 14 Position of A relative to B : Velocity of A relative to B : Acceleration of A relative to B : A B o x y
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