TWO AND THREE DIMENSIONAL MOTION formula
Scalar or Vector?
To explain the difference we use two words: 'magnitude' and 'direction'. By magnitude we mean how much of the quantity is there. By direction we mean is this quantity having a direction which defines it. Physical quantities which are completely specified by just giving out there magnitude are known as scalars. Examples of scalar quantities are distance, mass, speed, volume, density, temperature etc. Other physical quantities cannot be defined by just their magnitude. To define them completely we must also specify their direction. Examples of these are velocity, displacement, acceleration, force, torque, momentum etc.
Vector Addition
Parallelogram law of vector addition
If we were to represent two vectors magnitude and direction by two adjacent sides of a parallelogram. The resultant can then be represented in magnitude and direction by the diagonal. This diagonal is the one which passes through the point of intersection of these two sides.
Resolution of a Vector
It is often necessary to split a vector into its components. Splitting of a vector into its components is called resolution of the vector. The original vector is the resultant of these components. When the components of a vector are at right angle to each other they are called the rectangular components of a vector.
Rectangular Components of a Vector
As the rectangular components of a vector are perpendicular to each other, we can do mathematics on them. This allows us to solve many real life problems. After all the best thing about physics is that it can be used to solve real world problems.
Note: As it is difficult to use vector notations on the computer word processors we will coin our own notation. We will show all vector quantities in bold. For example 'A' will be scalar quantity and 'A' will be a vector quantity.
Let Ax and Ay be the rectangular components of a vector A
then
A = Ax + Ay this means that vector A is the resultant of vectors Ax and Ay
A is the magnitude of vector A and similarly Ax and Ay are the magnitudes of vectors Ax and Ay
As we are dealing with rectangular components which are at right angles to each other. We can say that:
A = (Ax + Ay)1/2
Similarly the angle Q which the vector A makes with the horizontal direction will be
Q = tan-1 (Ax / Ay)
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