Explain with examples of scalar quantities and vector quantities

Physical Quantities

1.1

Physical Quantities

	What is physics?
	A knowledge to find a rational explanation (why and how) of the nature of matter, energy and natural phenomena. Involves the quantity being measured, formula and matter Many theories are proved through calculations Use of standard units

	Field of Physics
	Heat Light Electrical and electronics Astronomy Nuclear Biophysics Wave Force and motion Plasma physics

	Physical quantities
	contains magnitude and unit can be measured

Base quantities :	Derived quantities :
Physical quantities that cannot be defined in terms of other physical quantities.	A physical quantity that is derived by a combination of base quantities. Can be done by multiplication, division or both.

Example :	Example :
length, \(\text{l}\) (\(m\)) mass, \(\text{m}\) (\(kg\)) time, \(\text{t}\) (\(s\)) temperature, \(\text{T}\) (\(K\)) current, \(\text{I}\) (\(A\))	(Other than base = derived) area, \(\text{l}\times\text{l}\) (\(m^2\)) volume, \(\text{v}=\text{l}\times\text{l}\times\text{l}\) (\(m^3\)) density, \(\dfrac{\text{m}}{\text{v}}\) (\(kgm^{−3}\)) speed, \(\dfrac{\text{l}}{\text{t}}\) (\(ms^{−1}\)) acceleration, \(\dfrac{\text{speed}}{\text{t}}\) (\(ms^{−2}\))

Standard form

Standard form is a way of writing down very large or very small numbers easily and without using lots of zeros. We sometimes call it scientific notation.

\(A\times10^n\;,\;1\leq A < 10\)

	Question examples

	Example 1 : Convert \(135\) to standard numbers. \(\;\curvearrowleft\curvearrowleft\\1\,3\,5\;. \rightarrow 1.35 \times 10^2\) two decimal move to the left \(=\) \(+\)

	Example 2 : Convert \(0.00008\) to standard numbers. \(\;\;\curvearrowright\curvearrowright\curvearrowright\curvearrowright\curvearrowright\\0.0\;\;0\;\;0\;\,0\,\;8 \rightarrow 8 \times 10^{-5}\) five decimal move to the right \(=\) \(-\)

	Prefix
	Prefixes are the preceding factor used to represent very small and very large physical quantities in SI units.

Prefix	Symbol	Standard form
tera	\(T\)	\(10^{12}\)
giga	\(G\)	\(10^{9}\)
mega	\(M\)	\(10^{6}\)
kilo	\(k\)	\(10^{3}\)
hecto	\(h\)	\(10^{2}\)
deka	\(da\)	\(10^{1}\)
deci	\(d\)	\(10^{-1}\)
centi	\(c\)	\(10^{-2}\)
milli	\(m\)	\(10^{-3}\)
micro	\(µ\)	\(10^{-6}\)
nano	\(n\)	\(10^{-9}\)
pico	\(p\)	\(10^{-12}\)

No prefix \(\rightarrow\) Prefix ( \(\div\) )

Example : Convert \(200\,m\) to \(km\).

\(200\div10^3=0.2\,km\)

Prefix \(\rightarrow\) No prefix ( \(\times\) )

Example : Convert \(0.2\,km\) to \(m\).

\(0.2\times10^3=200\,m\)

Scalar quantity	Vector quantity
Physical quantity that has only magnitude	Physical quantity that has both magnitude and direction
Example: Distance, speed, time, mass, energy	Example: Displacement, velocity, weight, force

Physical Quantities

1.1

Physical Quantities

	What is physics?
	A knowledge to find a rational explanation (why and how) of the nature of matter, energy and natural phenomena. Involves the quantity being measured, formula and matter Many theories are proved through calculations Use of standard units

	Field of Physics
	Heat Light Electrical and electronics Astronomy Nuclear Biophysics Wave Force and motion Plasma physics

	Physical quantities
	contains magnitude and unit can be measured

Base quantities :	Derived quantities :
Physical quantities that cannot be defined in terms of other physical quantities.	A physical quantity that is derived by a combination of base quantities. Can be done by multiplication, division or both.

Example :	Example :
length, \(\text{l}\) (\(m\)) mass, \(\text{m}\) (\(kg\)) time, \(\text{t}\) (\(s\)) temperature, \(\text{T}\) (\(K\)) current, \(\text{I}\) (\(A\))	(Other than base = derived) area, \(\text{l}\times\text{l}\) (\(m^2\)) volume, \(\text{v}=\text{l}\times\text{l}\times\text{l}\) (\(m^3\)) density, \(\dfrac{\text{m}}{\text{v}}\) (\(kgm^{−3}\)) speed, \(\dfrac{\text{l}}{\text{t}}\) (\(ms^{−1}\)) acceleration, \(\dfrac{\text{speed}}{\text{t}}\) (\(ms^{−2}\))

Standard form

Standard form is a way of writing down very large or very small numbers easily and without using lots of zeros. We sometimes call it scientific notation.

\(A\times10^n\;,\;1\leq A < 10\)

	Question examples

	Example 1 : Convert \(135\) to standard numbers. \(\;\curvearrowleft\curvearrowleft\\1\,3\,5\;. \rightarrow 1.35 \times 10^2\) two decimal move to the left \(=\) \(+\)

	Example 2 : Convert \(0.00008\) to standard numbers. \(\;\;\curvearrowright\curvearrowright\curvearrowright\curvearrowright\curvearrowright\\0.0\;\;0\;\;0\;\,0\,\;8 \rightarrow 8 \times 10^{-5}\) five decimal move to the right \(=\) \(-\)

	Prefix
	Prefixes are the preceding factor used to represent very small and very large physical quantities in SI units.

Prefix	Symbol	Standard form
tera	\(T\)	\(10^{12}\)
giga	\(G\)	\(10^{9}\)
mega	\(M\)	\(10^{6}\)
kilo	\(k\)	\(10^{3}\)
hecto	\(h\)	\(10^{2}\)
deka	\(da\)	\(10^{1}\)
deci	\(d\)	\(10^{-1}\)
centi	\(c\)	\(10^{-2}\)
milli	\(m\)	\(10^{-3}\)
micro	\(µ\)	\(10^{-6}\)
nano	\(n\)	\(10^{-9}\)
pico	\(p\)	\(10^{-12}\)

No prefix \(\rightarrow\) Prefix ( \(\div\) )

Example : Convert \(200\,m\) to \(km\).

\(200\div10^3=0.2\,km\)

Prefix \(\rightarrow\) No prefix ( \(\times\) )

Example : Convert \(0.2\,km\) to \(m\).

\(0.2\times10^3=200\,m\)

Scalar quantity	Vector quantity
Physical quantity that has only magnitude	Physical quantity that has both magnitude and direction
Example: Distance, speed, time, mass, energy	Example: Displacement, velocity, weight, force

Physical Quantities

Physical Quantities

Chapter : Measurement

Topic : Explain with examples of scalar quantities and vector quantities

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