Scalars and Vectors

Scalars:

Have only magnitude.

Are added algebraically.

Examples: temperature, mass

Vectors:

Have magnitude and direction.

Are added through the triangle law.

Examples: velocity, force

NOTE: Vectors can be moved around in space as long as their

magnitude (length) and direction remain unchanged. This property

is utilized when adding vectors.

Methods for adding vectors

Graphical method:

Parallelogram method

Triangle method

Polygon method

Analytic method:

Through breaking the vectors into → components

Experimental method:

By using the → force table

Parallelogram method (graphical)

Place the two vectors,⃗A andB⃗ to be added with their tails

touching to form a vertex of a parallelogram, with the vectors as

two of its adjacent sides.

Complete the other two sides of the parallelogram.

The diagonal drawn joining the initial vertex to its opposite

vertex gives the resultant vector ⃗R= A⃗ + B⃗ , as shown in the

diagram.

Analytic method

Experimental method: force table

Hang specific masses with strings from a ring , at specific angles

from a force table. The tensions in the strings due to hanging

masses act as our vectors.

Add masses with another string on the ring. Adjust mass and

angle of this one in such that it centers ring at the peg at the center

of force table. The force balances the resultant of the other forces,

and is the exact opposite of the resultant force in direction, and

exactly equal to resultant force in magnitude.

End of Theory