Students can go through AP State Board 9th Class Physical Science Notes Chapter 12 Units and Graphs to understand and remember the concept easily.

## AP State Board Syllabus 9th Class Physical Science Notes Chapter 12 Units and Graphs

→ A unit is a standard measure used for comparing measurements.

→ Units should be placed right side of the magnitude of every physical quantity.

For Example 2 kilograms, 100 grams.

→ The main fundamental quantities are mass (m), length (l), time (t).

→ Fundamental quantities are those physical quantities that cannot be expressed in terms of other quantities.

→ Fundamental quantities are also called base quantities.

→ Scientists evolved different types of measuring systems such as FPS, CGS, MKS, etc.

- FPS System: Foot – Pound – Second.
- CGS System: Centimeter – Gram – Second.
- MKS System: Meter – Kilogram – Second.

→ SI System is an International System of units.

→ In addition to mass, length, and time some other fundamental quantities were added to the SI system.

→ Units in SI System:

- Length – Meter (m)
- Mass – Kilogram (kg)
- Time – Second (s)
- Electricity – Ampere (A)
- Light intensity – Candela (Cd)
- Quantity of substance – Mole (Mol)
- Temperature – Kelvin (K)
- Plane angle – Radian (rad)

→ The quantities that are obtained by combining fundamental quantities either by multiplication or division or both operations are called derived quantities.

→ Some derived quantities are speed, velocity, area, volume, density, acceleration, force, pressure, etc.

→ Derived units are units of measurements derived from the fundamental units.

→ Some examples of derived units are

- Area – m
^{2} - Volume – m
^{3} - Speed – m/s
- Velocity – m/s
- Acceleration – m/s
- Force – \(\frac{\mathrm{kg}}{\mathrm{m} / \mathrm{s}^{2}}=\frac{\mathrm{kg} \cdot \mathrm{s}^{2}}{\mathrm{~m}}\) , etc.

→ We need to convert units of a physical quantity into a single system to compare both values.

For example: To compare 1500 m and 1.5 km Convert km into meters.

Then 1500 m = 1500 m, 1.5 km = 1500 m

Hence both values are equal.

→ 1000 m = 1 km

1000 is prefixed to meter called as ‘Kilo’

→ 1 km/hr = \(\frac{5}{18}\)m/s

→ Meter is the distance travelled by light in a vacuum in \(\frac{1}{299792458}\) seconds

→ There are some rules to follow while writing units.

→ A pictorial form of representation that shows the relation between two quantities can be called a graph.

→ The expressed quantity depends on the independent and dependent variables taken for plotting the graph.

→ Generally, independent variables are controlled or decided by us, but dependent variables are changed due to the change independent variable.

→ The thick horizontal line on the graph paper is called X-axis.

→ The thick vertical line on the graph paper is called Y-axis.

→ The Independent variable should be taken on the x-axis, whereas the dependent variable is on the y – axis.

→ The range is the difference between the highest value and lowest value of the data.

Range = highest value – lowest value.

→ Scale on X-axis = \(\frac{\text { Range }}{\text { The number of grids on } \mathrm{X} \text { -axis }}\)

Scale on y-axis = \(\frac{\text { Range }}{\text { The number of grids on } \mathrm{Y} \text { -axis }}\)

→ Axes should be named with the quantity taken on it along with their units.

→ The values taken as pairs such as (x_{1}, y_{1}), (x_{2}, y_{2}), are called data points.

→ If a graph is curved in shape, it is called a curved graph.

→ If a graph is a straight line, it is called a straight line graph.

→ Both curved, straight-line graphs are called line graphs.

→ Hooke’s Law: Elongation of the spring is proportional to mass.

The graph of extension and mass is a straight-line graph and it indicates the relationship of direct proportional between extension and mass.

→ Direct proportion:

- The initial values should be counted as “0”.
- The ratio of any pair has to be constant.
- If the value of one quantity increases, the value of the second quantity also increases.

→ Inverse proportional:

- The value of one quantity should be “0”, the value of the second quantity cannot be defined, it can be infinite.
- The product of any two pairs should be constant.
- The value of one quantity increases, the value of the second quantity should be decreased.

→ Pressure ∝ \(\frac{1}{\text { Volume }}\) [inversely proportionally]

The graph of pressure and volume is parabolic in shape.

→ Slope of the straight line = \(\frac{\text { Change in } y \text { -coordinates }}{\text { Change in } x \text { -coordinates }}=\frac{\text { rise }}{\text { run }}\) (or) tan θ = \(\frac{\Delta y}{\Delta x}\)

→ The slope of the graph is denoted by “m”.

→ The slope of the straight line increases along with the increase of angle.

→ The slope of the X-axis is zero.

→ Slope can be determined by coordinates of x, y, or by the angle of a straight line with the X-axis.

→ A curved line graph has an infinite number of slopes.

→ We can calculate the slope at any point on the curve by drawing a tangent to it.

→ The ratio of the Y and X-axis represents slope.

→ The product of quantities on the Y and X-axis is said to be an area of the graph.

→ Unit: A unit is a standard measure used for comparing measurements.

→ Fundamental: Fundamental quantities are those physical quantities that quantities cannot be expressed in terms of other quantities.

→ Basic quantities: Fundamental quantities are also called basic quantities.

→ FPS: Foot, Pound, Second.

→ CGS: Centimeter, Gram, Second.

→ MKS: Meter, Kilogram, Second.

→ SI System: International System of units.

→ Derived quantities: The quantities that are obtained by combining fundamental quantities either by multiplication or division or both operations are called derived quantities.

→ Some fundamental: Length, Mass, Time, Electricity, Light intensity, Quantity of quantities substance, Temperature, Plane angle.

→ Some derived quantities: Area, Volume, Density, Velocity, Acceleration, Force, Pressure.

→ Fundamental Units: Meter, Kilogram, Second, Ampere, Candela, Mole, Kelvin, Radian.

→ Derived Units: Derived units are units of measurement derived from the fundamental units. m^{2}, m^{3}, kg/m^{3}, m/s, m/s^{2}.

→ Meter: Meter is the distance travelled by light in a vacuum in \(\frac{1}{299792458}\) seconds

→ Graph: A pictorial form of representation that shows the relation between two quantities can be called a graph.

→ Independent: The variable which is controlled or decided by us to plot a graph variable is called the independent variable.

→ Dependent variable: The variable which is changed due to the change in the independent variable is called the dependent variable.

→ Grids: Grids of one square centimeter form by the intersection of thick lines and one square millimeter grid form with the intersection of thin lines in graph paper.

→ X-axis: The thick horizontal line on the graph paper is called X-axis.

→ Y-axis: The vertical thick line is called Y-axis.

→ Range: The highest value – the lowest value.

→ Scale: The interval taken to point the values on the axes is called scale.

Scale = \(\frac{\text { Range }}{\text { The number of grids on the axis }}\)

→ Data points: The values are to be taken as pairs in order to mark them as points on the graph such as (x, y) is called data points.

→ Curved line graph: If the line in a graph is in a curved shape, then the graph is called a curved line graph.

→ Straight-line graph: If the line in a graph is a straight line, then the graph is called a straight-line graph.

→ The slope of a straight: The ratio between the change in y-coordinates and the line graph x – coordinates gives the slope of the straight-line graph.

→ Slope = \(\frac{\text { Change in } y \text { -coordinates }}{\text { Change in } x \text { -coordinates }}=\frac{\text { rise }}{\text { run }}\) (or) tan θ = \(\frac{\Delta y}{\Delta x}\)

The slope is denoted with ‘m’.

→ Area of graph: The product of the physical quantity of the Y-axis and X-axis is said to be an area of the graph.

→ Robert Hooke:

- Born: 28th July (O.S. 18 July) 1635
- Died: 3rd March 1703 (aged 67)
- Nationality: English
- Alma mater: Wadham College, Oxford
- Known for: Hooke’s law, Microscopy,
- Coining the word ‘cell’
- Fields: Physics and Chemistry
- Institutions: Oxford University Academic
- Advisors: Robert Boyle
- Influences: Richard Busby