Physics Chapter 2.1: Physical Quantities and Units

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Questions and Answers

Define a physical quantity.

A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit.

Which of the following are base quantities in the System International of Units (SI)?

Length (correct)

Area

Time (correct)

Mass (correct)

The SI unit for mass is ________________.

kilogram

The prototype kilogram based on a metal cylinder is still used today.

False Signup and view all the answers

Match the following prefixes with their corresponding symbols and factors:

pico = p nano = n micro = µ milli = m kilo = k mega = M giga = G tera = T Signup and view all the answers

How can accuracy be enhanced when doing estimations?

By dividing the figure into small squares and defining the area of each square. Signup and view all the answers

How should we read the volume of a liquid with a meniscus?

Read off the scale at the bottom of the meniscus if concave and at the top if convex. Signup and view all the answers

Which of the following instruments is more accurate for time measurements?

Digital stopwatch Signup and view all the answers

Period of oscillation in a pendulum is affected by the mass of the bob.

False Signup and view all the answers

What is the result of 5.24 + 4.1?

9.3 Signup and view all the answers

What is the result of 26.28 - 19.2?

7.1 Signup and view all the answers

Calculate the sum of 17.2, 17.5, and 17.4, then divide the result by 3.

17.4 Signup and view all the answers

What is the result of 24 × 14.8?

360 Signup and view all the answers

What is the result of 82 ÷ 12.3?

6.7 Signup and view all the answers

Calculate 34.6 divided by 20.

1.73 Signup and view all the answers

What is the speed of an object that traveled 10 m in 2.0 s?

5.0 m/s Signup and view all the answers

Which term best describes an apparatus that has difficulty reproducing the same reading?

Imprecise Signup and view all the answers

Study Notes

Physical Quantities and Units

A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit.
Example: 4.5 m is a physical quantity, where 4.5 is the numerical value and m is the unit.

Base Quantities

The System International of Units (SI) defines 7 base quantities and units:
- Length: meter (m)
- Mass: kilogram (kg)
- Time: second (s)
- Electric current: ampere (A)
- Temperature: kelvin (K)
- Amount of substance: mole (mol)
- Luminous intensity: candela (cd)
The definitions of base quantities are based on specific physical measurements that can be reproduced accurately in laboratories around the world.

Derived Quantities

Derived quantities are physical quantities that are derived from a combination of base units using a defining equation.
Examples:
- Area: length × width (m²)
- Volume: length × width × height (m³)
- Speed: distance / time (m/s)

Prefixes

Prefixes are used to indicate a decimal multiple or sub-multiple of a unit.
Examples:
- Pico (p): 10^(-12)
- Nano (n): 10^(-9)
- Micro (μ): 10^(-6)
- Milli (m): 10^(-3)
- Centi (c): 10^(-2)
- Deci (d): 10^(-1)
- Kilo (k): 10^3
- Mega (M): 10^6
- Giga (G): 10^9
- Tera (T): 10^12

Unit Conversion

Unit conversion is the process of converting a quantity from one unit to another similar unit.
Example: converting 0.800 g/cm³ to kg/m³

Measuring Instruments

Various measuring instruments are used to measure different physical quantities, such as:
- Measuring cylinder: measures volume of liquids
- Metre rule: measures length
- Digital calipers: measures length and diameter
- Digital micrometer screw gauge: measures small lengths
- Electronic balance: measures mass
- Stopwatch: measures time

Area Measurements

Area measurements can be done using:
- Formulae for regular shapes (e.g., square, rectangle, triangle, circle)
- Estimation by dividing the figure into small squares
- Tracing the outline of the figure and counting the number of squares

Volume Measurements

Volume measurements can be done using:
- Measuring cylinder: measures volume of liquids
- Pipette: measures specific volumes of liquids
- Burette: measures volume of liquids with high accuracy

Time Measurements

Time measurements can be done using:
- Stopwatch: measures short intervals of time
- Pendulum: measures the period of oscillation
- Atomic clock: measures time with high accuracy### Significant Figures and Rules for Rounding Off
The number of significant figures is directly related to the precision of the measuring instrument.
A calculated value can be no more precise than the values used to obtain it.
When giving answers, quote to the same number of significant figures as the least precise measurement.

Rules for Rounding Off

Raw data are measurements taken directly from a measuring instrument, expressed to a fixed number of decimal places dictated by the units used and the precision of the instrument.
Processed data are readings obtained from the calculation of one or more sets of raw data.
Rules for rounding off in calculation of processed data:
- Addition and subtraction: refer to decimal place, answer has same number of decimal places as the least number of decimal places or place value in any of the numbers.
- Multiplication and division: refer to significant figure, answer has same number of significant digits as the least number of significant digits in any one of the numbers.

Practice Exercises

Answers to practice exercises:
- a. 5.24 + 4.1 = 9.3
- b. 26.28 – 19.2 = 7.1
- c. 17.2 + 17.5 + 17.4 = 17.4
- d. 24 × 14.8 = 360
- e. 82 ÷ 12.3 = 6.7
- f. 34.6 ÷ 20 = 1.73

The Use of Algebra (Quantity and Number Algebra)

Scientific equations are statements written in the form of complete sentences, using universal shorthand (Quantity Algebra).
Good practice: initial substitution of original units facilitates comprehension and checking.
Bad practice: omission of original units when substituting leads to incorrect statements.

Advanced Topic: The Ticker Tape Timer

The ticker-tape timer is an electrical device used in certain Physics experiments to measure short intervals of time.
It marks short intervals of time by making 50 dots per second on a paper tape being pulled past it.
Between two consecutive dots, there is a time interval of 1/50 s or 0.02 s.

Advanced Topic: Accuracy and Precision

Accuracy refers to the degree of closeness to the true value.
Precision refers to the degree to which an instrument or process will repeat the same value.
An inaccurate apparatus has a systematic error and is unable to provide a true value of the reading.
An imprecise apparatus has difficulty reproducing the same reading; hence it will make many random errors.