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SCALARS AND VECTORS

SCALARS AND VECTORS. SCALARS AND VECTORS. Scalar is a simple physical quantity that is not changed by coordinate system rotations or translations. Expressing a scalar quantity we give it simply with a number and a unit (for example, 12 kg) .

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SCALARS AND VECTORS

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  1. SCALARS AND VECTORS

  2. SCALARS AND VECTORS • Scalar is a simple physical quantity that is not changed by coordinate system rotations or translations. • Expressing a scalar quantity we give it simply with a number and a unit (for example, 12 kg). • If a quantity has both a magnitude and direction, it is called a vector.

  3. SCALARS AND VECTORS

  4. Vectors • Vectors are equal when they have the same magnitude and direction, irrespective of their point of origin. A A A

  5. SUM OF TWO VECTORS C= A + B B A B If two vectors have the same direction, their resultant has a magnitude equal to the sum of their magnitudes and will also have the same direction.

  6. SUM OF TWO VECTORS C= A + B A B B If two vectors have the opposite direction, their resultant has a magnitude equal to the subtraction of their magnitudes; direction of the sum is equivalent to the direction of longer vector (to the bigger magnitude).

  7. sum of two vectors by a graphical method B A C=A+B B Two vectors A and B are added by drawing the arrows which represent the vectors in such a way that the initial point of B is on the terminal point of A. The resultant C = A + B, is the vector from the initial point of A to the terminal point of B.

  8. Polygon method

  9. Parallelogram method In the parallelogram method for vector addition, the vectors are translated, (i.e., moved) to a common origin. The resultant R is the diagonal of the parallelogram drawn from the common origin.

  10. Method of components • The components of a vector are those vectors which, when added together, give the original vector. • The sum of the components of two vectors is equal to the sum of these two vectors.

  11. Rectangular components • In all vector problems a natural system of axes presents itself. In many cases the axes are at right angles to one another. • Components parallel to the axes of a rectangular system of axes are called rectangular components. • In general it is convenient to call the horizontal axis X and the vertical axis Y. • The direction of a vector is given as an angle counter-clockwise from the X-axis.

  12. Rectangular components • The magnitude of A,|A|, can be calculated from the components, using the Theorem of Pythagoras: • and the direction can be calculated using

  13. Multiplication of vectors bypositive scalar • Scalar multiplication of vector by a positive real number multiplies the magnitude of the vector without changing its direction. a 2a 3a

  14. Multiplication of vectors by negative scalar • Scalar multiplication of vector by a negative real number multiplies the magnitude of the vector and changes its direction into opposite directions. a -2a -3a

  15. Division of vectors by scalars • Scalar dividing of vector by a real number is equal to multiplication with reciprocal (or multiplicative inverse) of that number. a÷2 = ½ x a a b÷(-3) = -1/3 x b b

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