Handouts for Chapter I / III
System International or SI units for measurement are the meter, kilogram (kg) and
second. This is the universally accepted metric system and is superior because it is decimal
based. To convert from unit to another in this system like from gm to kg, we need to go only in
multiples of 10. Only similar units can be added or subtracted together, for eg 2 km + 3 km is
correct; 2 km + 3 miles cannot be added unless they are converted to proper units.
The speed of light in vacuum is a universal constant and is independent of all external forces or
disturbances and is 299,792,458 m/sec. The standard meter is thus defined as the distance that
light travels in (1/299,792,458) seconds. The standard second is defined as per the vibrations of
a cesium-133 atomic clock and is the time in which the atom undergoes 9,192,631,770 wave
cycles. A platinum-iridium bar is kept in France is considered the standard kilogram of mass. All
other measurements like our meter scale, weights, clocks are defined by comparison with these
universally accepted standards.
Refer to page 4 of chapter I, table 1.2 for standard prefixes in SI units, and to pg 5 for the
reasoning strategy for converting between units. Make sure that all the units appearing in the
conversion are taken care of.
The fundamental dimensions for mass, length and time are M, L, and T. All physical
quantities are a combination of one or more of these dimensions. Every equation in physics
should be dimensionally equal on both sides to be correct. Refer to pg 6 of chapter I for detail.
Refer to math review for trigonometric functions. Refer to pg 8 of chapter I for inverse
trigonometric functions. Keep your calculator always in the degree mode.
If sin () = x, then  = sin(x); for example, sin (900) = 1 or 900 = sin-1(1)
If tan () = y, then  = tan(y); for example, tan (450) = 1 or 450 = tan-1(1)
If cos () = z, then  = cos(z); for example, cos (600) = 0.5 or 600 = cos-1(0.5)
Vectors
Vectors have both magnitude and direction, whereas scalars have only magnitude. For
example, velocity, acceleration, force, and displacement are vectors, and speed, distance,
volume, area, temperature, energy, time are scalars. Whenever in doubt, ask yourself this
question, does this physical quantity being stated require the question “in what direction?”
The direction of arrow gives direction of vector and by convention its length is
proportional to its magnitude. Any direction is always with reference to some frame or
standard. We usually refer to velocity or displacement with reference to an x-y axis, with the
direction being the angle the vector makes with the positive side of the x-axis. Directions
are also given in terms of north, south, east, and west. By convention, the east is along the + x
axis. Also by convention, in the text book, all bold lettering refers to vectors. For example A, B or
R are vectors, then their magnitudes (scalar values) are given as A, B or R respectively.
Vectors can be added or subtracted like scalars only if they are collinear or in the same line.
Other wise they are to be added using the vector methods. In case of perpendicular vectors,
the resultant vector can be found using the Pythagorean theorem. However for other
vectors, either the graphical method or component method is used. The latter is practical and
best way. Every vector (2-D) can be resolved as the sum of two components, one in the x and
one in the y direction.
A vector can be zero only if (all) both its x and y components are zero. A non-zero vector can
have a zero x or zero y component if it is parallel to the y-axis or x-axis respectively. The
resultant of two non-zero vectors can never be zero, unless they are collinear vectors. Two
vectors can be equal only if (all) both their x and y components are equal. Two vectors are equal
only if they have both the same magnitude and direction. Vectors are always added or subtracted
after arranging them with head to tail.
There can be both scalar and vector components. The scalar values simply give magnitude of the
vector components. If vector component Ax has a value of 10 km and is pointing in the –x
direction, then its scalar component Ax has a negative value of –10 km. After resolving vectors in
to components use the reasoning strategy given in pg 17 of chapter I for vector addition and
subtraction. Refer also to examples of solved problems 7,8,9 and 10 and their solutions in
chapter I, pg 14-19. To get an idea of pictorial representation of vectors and resolution of vectors
in to components refer to figures 1.16, 1.17, 1.18, 1.2 and 1.21, pg 13, 14 and 16.