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[accordion title=”1. Base and Derived Quantities”]

• Physical quantities are classified as base (or fundamental) quantities and derived quantities.
  7 base quantities are chosen to form the base units.

• Any other physical quantities can be derived from these base quantities. These are called derived quantities.

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[accordion title=”2. Prefixes”]

• Prefixes are attached to a unit when dealing with very large or very small numbers.

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[accordion title=”3. Homogeneity of A Physical Equation”]

• A physical equation is said to be homogeneous if each of the terms, separated by plus, minus, equality or inequality signs has the same base units.

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[accordion title=”4. Uncertainty”]

• Absolute uncertainty of a measurement of $$x$$ can be written as $$\Delta x$$. This means that true value of the measurement is likely to lie in the range $$x-\Delta x$$ to $$x + \Delta x$$.
• Fractional uncertainty = $$\frac{\Delta x}{x}$$
• Percentage uncertainty = $$\frac{\Delta x}{x}\times100%$$
• If the values of two or more quantities such as $$a$$ and $$b$$ are measured and then these are combined to determine another quantity $$Y$$, the absolute or percentage uncertainty of $$Y$$ can be calculated as follows:
  • If $$Y = a\pm b$$, then  $$\Delta Y = \Delta a+\Delta b$$
  • If $$Y = ab$$ or $$Y = \frac{a}{b}$$ , then  $$\frac{\Delta Y}{Y} =\frac{\Delta a}{a}+\frac{\Delta b}{b}$$
  • If $$Y = a^n$$ then  $$\frac{\Delta Y}{Y} = n\frac{\Delta a}{a}$$

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[accordion title=”5. Errors”]

• Systematic errors are errors that, upon repeating the measurement under the same conditions, yield readings with error of same magnitude and sign.
• Random errors are errors that, upon repeating the measurement under the same conditions, yield readings with error of different magnitude and sign.

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[accordion title=”6. Accuracy and Precision”]

• The accuracy of an experiment is a measure of how close a measured value is to the true value. It is a measure of the correctness of the result.
• The precision of an experiment is a measure of how exact the result is without reference to what that the result means. It is a measure of how reproducible the results are, i.e. it is a measure of how small the uncertainty is.

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[accordion title=”7. Vectors”]

• A vector quantity has magnitude and direction.
• A scalar quantity has magnitude only.
• Addition of vectors in 2D: $$\vec{a}+\vec{b}=\vec{c}$$

• Methods of finding magnitudes of vectors:
  1. resolution of vectors into perpendicular components
  2. by scale drawing
  3. using:
     sine rule: $$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$$
     cosine rule: $$a^2 = b^2 + c^2-2bc \cos \alpha$$

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