Week2 - FIRST YEAR PHYSICS FIRST PHYS141 LECTURER: Dr....

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FIRST YEAR PHYSICS FIRST YEAR PHYSICS PHYS141 LECTURER: Dr. Carey Freeth Rm 4.110 Ph. 02 42214798 Email: carey_freeth@uow.edu.au The description of motion is now extended to the more general cases of motion in two and three dimensions by using vectors and the one dimensional equations derived previously. Vectors. A quantity that has both magnitude and direction In these lectures, the Cartesian (or rectangular) coordinate system will be used. Vector quantities are usually denoted by bold type face e.g. B or by . In these lectures, both notations will be used. r B
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Properties of Vectors Reading Ex. 1.7 - 1.9 Young & Freedman The Addition Law for Vectors Consider the addition of the displacement vectors A and B . We see that resultant displacement vector C , is the sum of the two successive displacements A and B . Thus, C = A + B ( Vector law for addition ). Note: The sum of the magnitudes of A and B does not equal the magnitude of C unless A and B are in the same direction.
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To manipulate vectors in two or three dimensions mathematically it is necessary to find the components of the vectors in the coordinate system being used. Any vector can be expressed in terms of their components and the summation of vectors is simply an addition of the component vectors; parallel to the x axis parallel to the y axis parallel to the z axis. since the components are in the same direction (or in the opposite direction which is taken into account by being assigned -ve). Components of a Vector. The projection of a vector on an axis or line is called a component. In the rectangular coordinate system the projection of a vector A on the axes are designated as A x , A y and A z . Thus in the example above for displacement vectors, the coordinates of P 1 can be denoted by (x 1 , y 1 ) and similarly for P 2 & P 3 so the components of the vectors are: A x = x 2 - x 1 A y = y 2 - y 1 B x = x 3 - x 2 B y = y 3 - y 2 C x = x 3 - x 1 C y = y 3 - y 1 and A x + B x = x 2 - x 1 + x 3 - x 2 = x 3 - x 1 = C x .
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Hence C = A + B implies both C x = A x + B x and C y = A y + B y . The magnitude of a vector is then given by; (PYTHAGORAS’S THEOREM) and the direction , ! , relative to the x axis is given by tan ! = A y A x . A = A x 2 + A y 2 Unit Vectors When writing vectors in terms of their components, it is convenient to define a unit vector which gives the direction of the individual components. In rectangular coordinates, we define i , j , & k (hand writing :- ) to be the unit vectors which have a magnitude of 1 and point in the x, y, z directions respectively. ˆ i , ˆ j & ˆ k Hence, a general vector, A , can be written as A = A x i + A y j + A z k . (e.g. A = 3 i + 4 j - 7 k) The sum of two vectors is obtained analytically by C = A + B = (A x i + A y j + A z k ) + (B x i + B y j + B z k ) = (A x + B x ) i + (A y + B y ) j + (A z + B z ) k . Properties of Vectors Reading Ex. 1.9 Young & Freedman
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Velocity and Acceleration Vectors The expressions we had for the one dimensional case can be extend to the two and three dimensional cases by representing the displacement vector as " r = r 2 - r 1 , where r 2 and r 1 are the position vectors in two or three dimensions.
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This note was uploaded on 08/20/2010 for the course PHYS 141 taught by Professor Xxx during the One '09 term at University of Wollongong, Australia.

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Week2 - FIRST YEAR PHYSICS FIRST PHYS141 LECTURER: Dr....

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