P0IITU03 - Motion in 2D

P0IITU03 - Motion in 2D - Motion in 2-D 1. Vectors 2....

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Unformatted text preview: Motion in 2-D 1. Vectors 2. Projectile Motion 3. Circular Motion 4. Relative Motion Galileo Vectors An object moves from point A to point B along the curved path shown. Supposing that we are not interested in the actual path followed but only in the result: That the object was displaced from A to B. How do we represent this Displacement ? A B We represent it by an arrow: A B What information does the arrow give us? The length of the arrow is proportional to the distance between the endpoints and it points in the direction of the displacement. The displacement of an object is an example of a vector. The displacement of an object depends only on its starting point and its end point, it does not depend on the path taken. The two paths shown below correspond to the same displacement vector. A B If I start someplace, go right around our galaxy and come back to the starting point, the displacement is zero. It is a vector of length zero. Q . What is the relation between the displacement and the distance traveled? A. There is really no relation. The most you can say is that the distance is greater than or equal to the magnitude of the displacement. The magnitude of the displacement is not the distance. Displacement is a vector. We represent vectors by arrows. How do we describe vectors? We can specify a vector by its magnitude (length) and its direction (the angle it makes with a given direction, maybe North). When a particle moved along a line (motion in 1-D), positive displacement meant that it ended up at a point to the right of the starting point, negative displacement meant that it ended up to the left of the starting point. The sign gave us the direction, the magnitude the amount. Q . An object is displaced by 30m east. Where is it now located? A . The displacement does not tell us the particles position is unless we know where it started. One object underwent a displacement of 30m east starting at some point in chennai and another one, starting at some point in Mumbai. Both displacements are identical, but their positions are different. Resultant displacement Resultant displacement Imagine that after going from point A to point B, our object proceeds onto point C, taking the curved path shown. A B C a b The second displacement is also represented by an arrow, as shown. Let us call the first displacement a and the second one, b . Vectors are written in bold. The object went from A to C, via B. Let us call the resulting displacement c . It points from A to C. c is the result of a followed by b . Vector c is called the resultant of vectors a and b . a b c We write it symbolically as: c = a + b The plus sign stands for the operation place second vector so that its tail coincides with the head of the first, then join the tail of the first to the head of the second to get the resultant. It is not a plus in the usual sense. This is called Vector addition....
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This note was uploaded on 10/05/2011 for the course PHY 203 taught by Professor Grimaldi during the Spring '11 term at St. Mary NE.

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P0IITU03 - Motion in 2D - Motion in 2-D 1. Vectors 2....

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