SCALARS AND VECTORS SCALARS AND VECTORS Scalar is

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). • If a quantity has both a magnitude and direction, it is called a vector.

SCALARS AND VECTORS Scalars (magnitude) Vectors (magnitude+direction) Speed Velocity Temperature Acceleration Distance Displacement Area Force Entropy Momentum Volume The electric field intensity Etc

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

SUM OF TWO VECTORS C= A + B A B 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.

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).

SUM OF TWO VECTORS BY A GRAPHICAL METHOD B A B + A C= 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.

Polygon method

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.

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.

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.

Rectangular components •

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

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 -2 a -3 a

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 b÷(-3) = -1/3 x b