Measurement of Length and Motion
Explore standard units of length (SI units), correct measurement techniques, reference points, and different types of motion including linear, circular, and oscillatory motion.
5.1 How do we Measure?
Measurement is a fundamental part of daily life. Non-standard units like handspan (balisht), strides, foot length, and finger widths (angula) vary from person to person because people have different body dimensions.
Measurement is expressed in two parts: a number and a unit. For example, if a table length is 13 handspans, 13 is the number and handspan is the unit selected for measurement[cite: 2].
Historical Measurement Units
India has a rich history of measurement systems dating back to ancient times[cite: 2]. Units mentioned in ancient literature include:
- Angula (finger width): Still used by traditional craftspeople like carpenters and tailors[cite: 2].
- Dhanusa and Yojana[cite: 2].
- Ruled scales excavated from archaeological sites of the Harappan Civilisation[cite: 2].
5.2 Standard Units
To avoid confusion caused by varying non-standard body units, countries across the world adopted a standard set of units called the International System of Units (SI units)[cite: 2].
SI Unit of Length
The standard SI unit of length is the metre (m)[cite: 2].
Smaller Units
$1\text{ m} = 100\text{ cm}$
$1\text{ cm} = 10\text{ mm}$[cite: 2]
Larger Units
$1\text{ km} = 1000\text{ m}$[cite: 2]
- Unit names (kilometre, metre, centimetre, millimetre) start with a lowercase letter, except at the beginning of a sentence[cite: 2].
- Symbols ($\text{km}, \text{m}, \text{cm}, \text{mm}$) are always lowercase and never pluralized with an 's'[cite: 2].
- Always leave a space between the number and the unit (e.g., $10\text{ cm}$)[cite: 2].
5.3 Correct Way of Measuring Length
When measuring length with a standard scale, follow these rules for accuracy:
- Placement of Scale: Place the scale in contact with the object along its length[cite: 2].
- Position of the Eye: Position your eye directly vertically above the point being measured to avoid parallax errors[cite: 2].
- Handling Broken Scales: If zero mark is damaged or broken, start from another full mark (e.g., $1.0\text{ cm}$) and subtract this initial value from the final reading at the end[cite: 2].
Example: Final reading $10.4\text{ cm} - \text{Initial reading } 1.0\text{ cm} = 9.4\text{ cm}$[cite: 2].
5.4 Measuring the Length of a Curved Line
A straight scale cannot directly measure a curved line[cite: 2]. To measure curved lengths (such as decorative arches or curved boundaries):
- Use a flexible measuring tape directly, OR[cite: 2]
- Use a thread along the curve, mark the ends, then straighten the thread and measure its length against a standard scale[cite: 2].
5.5 Describing Position & Reference Point
To specify the position or distance of an object accurately, it must be stated relative to a fixed point[cite: 2].
Example: Kilometre stones stating 'Delhi $70\text{ km}$' use Delhi as the reference point[cite: 2].
5.6 Moving Things (Rest vs Motion)
Motion
An object is in motion if its position changes with respect to a reference point over time[cite: 2].
Rest
An object is at rest if its position does not change with respect to a reference point over time[cite: 2].
State of rest or motion depends on the reference point chosen. Passengers inside a moving bus are at rest relative to each other, but in motion relative to objects outside the bus[cite: 2].
5.7 Types of Motion
| Type of Motion | Definition | Examples |
|---|---|---|
| Linear Motion | Motion of an object along a straight path[cite: 2]. | Falling eraser, marching soldiers in parade, pushing a box[cite: 2]. |
| Circular Motion | Motion of an object along a circular path[cite: 2]. | Whirling a stone tied to a string, merry-go-round[cite: 2]. |
| Oscillatory Motion | To-and-fro movement of an object about a fixed central position[cite: 2]. | Swinging pendulum, playground swing, vibrating metal strip[cite: 2]. |
| Periodic Motion | Motion that repeats itself after equal fixed intervals of time[cite: 2]. | Circular and oscillatory motions are periodic in nature[cite: 2]. |
Chapter Summary
- SI Unit of Length: Metre ($\text{m}$)[cite: 2].
- Conversion Factors: $1\text{ km} = 1000\text{ m}$, $1\text{ m} = 100\text{ cm}$, $1\text{ cm} = 10\text{ mm}$[cite: 2].
- Reference Point: A fixed point used to describe the position or state of motion of an object[cite: 2].
- Rest & Motion: Dependent on whether position changes relative to a reference point over time[cite: 2].
- Types of Motion: Linear (straight path), Circular (circular path), Oscillatory (to-and-fro)[cite: 2].
Exercises & Practice Questions
1. Which of the following is NOT a standard unit of measuring length?
Question: Express $1.5\text{ km}$ distance in metres[cite: 2].
Solution:
Since $1\text{ km} = 1000\text{ m}$[cite: 2]
$$1.5\text{ km} = 1.5 \times 1000\text{ m} = 1500\text{ m}$$
1. The motion of a car moving on a straight road is linear motion. — True[cite: 2]
2. $1\text{ km} = 100\text{ cm}$. — False (Correct: $1\text{ km} = 100,000\text{ cm}$)[cite: 2]