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
