chapter4 - Chapter 4 Motion in Two Dimensions Kinematics in...

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Chapter 4 Motion in Two Dimensions
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Kinematics in Two Dimensions Will study the vector nature of position, velocity and acceleration in greater detail Will treat projectile motion and uniform circular motion as special cases Discuss relative motion Introduction
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Position and Displacement The position of an object is described by its position vector, . The displacement of the object is defined as the change in its position. & r ' { ± & & & f i r r r Section 4.1
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General Motion Ideas In two- or three-dimensional kinematics, everything is the same as in one- dimensional motion except that we must now use full vector notation. Positive and negative signs are no longer sufficient to determine the direction. Section 4.1
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Average Velocity The average velocity is the ratio of the displacement to the time interval for the displacement. The direction of the average velocity is the direction of the displacement vector. The average velocity between points is independent of the path taken. This is because it is dependent on the displacement, which is also independent of the path. ' { ' & & avg t r v Section 4.1
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Instantaneous Velocity The instantaneous velocity is the limit of the average velocity as ǻ t approaches zero. As the time interval becomes smaller, the direction of the displacement approaches that of the line tangent to the curve. ' o ' { ' & & & 0 lim t d t dt r r v Section 4.1
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Instantaneous Velocity, cont The direction of the instantaneous velocity vector at any point in a particle s path is along a line tangent to the path at that point and in the direction of motion. The magnitude of the instantaneous velocity vector is the speed. The speed is a scalar quantity. Section 4.1
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Average Acceleration The average acceleration of a particle as it moves is defined as the change in the instantaneous velocity vector divided by the time interval during which that change occurs. f i avg f i t t t ± ' { ' ± v v v a & & & & Section 4.1
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Average Acceleration, cont As a particle moves, the direction of the change in velocity is found by vector subtraction. The average acceleration is a vector quantity directed along . ' & v ' ± & & & f i v v v Section 4.1
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Instantaneous Acceleration The instantaneous acceleration is the limiting value of the ratio as ǻ t approaches zero. The instantaneous equals the derivative of the velocity vector with respect to time.
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