P2F11-Week7-Barwick

P2F11-Week7-Barwick - Week 7 Motion in Two Dimensions Read...

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Week 7 Motion in Two Dimensions Read Sections 3.1 – 3.3
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Clicker problem l A package is dropped by an airplane traveling horizontally at 50 m/s at an altitude of 1000m. What is the initial velocity of package just after it leaves the plane? As usual, ignore wind resistance. l A) 50 m/s i B) -50 m/s j l C) 50 m/s i + 50 m/s j l D) 0 E) Cannot be determined
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Describing Motion motion in 2D or 3D l In two- or three-dimensional kinematics, everything is the same as as in one- dimensional motion except that we must now use full vector notation l Positive and negative signs are no longer sufficient to determine the direction of the vectors (displacement, velocity, acceleration)
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Position and Displacement l The position of an object is described by its position vector, l The displacement of the object is defined as the change in its position l ! r ! " # ! ! ! f i r r r
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Average Velocity l The average velocity is the ratio of the displacement to the time interval for the displacement l The direction of the average velocity is the direction of the displacement vector l The magnitude of the instantaneous velocity vector is the speed l The speed is a scalar quantity ! v ave = ! r f " ! r i t f " t i = ! r 2 " ! r 1 t 2 " t 1 = # ! r # t Just different notation
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Average Acceleration l 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. l As a particle moves, the direction of the change in velocity is found by vector subtraction l The average acceleration is a vector quantity directed along ! " # = ! " ! ! ! ! f i avg f i t t t v v v a ! = " ! ! ! f i v v v ! ! v
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Instantaneous Velocity l The instantaneous velocity is the limit of the average velocity as Δ t approaches zero l Equals the derivative of the position vector with respect to time ! " ! # = ! ! ! ! 0 lim t d t dt r r v l The instantaneous acceleration is the limiting value of average acceleration as Δ t approaches zero l Equals the derivative of the velocity vector with respect to time ! " ! # = ! ! ! ! 0 lim t d t dt v v a
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Producing An Acceleration l Various changes in a particle’s motion may produce an acceleration l The magnitude of the velocity vector may change l The direction of the velocity vector may change l Even if the magnitude remains constant l Both may change simultaneously
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Clicker quick question 1 Which of the following cannot possibly be accelerating? (A) An object moving with a constant speed (B) An object moving with a constant velocity (C) An object moving along a curve (D) An object moving along a straight line (E) Both B and D
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Clicker quick question 2 You tie a stone with a string and whirl it around in a circle. The acceleration of this stone is:
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This note was uploaded on 12/12/2011 for the course PHYS 2 taught by Professor Staff during the Fall '08 term at UC Irvine.

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P2F11-Week7-Barwick - Week 7 Motion in Two Dimensions Read...

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