# Measurement of Length and Motion

## Overview
In this chapter, students explore the methods and tools for measuring length and understanding different types of motion. They engage in real-life examples and activities to differentiate between units of measurement, learn to describe positions using reference points, and identify various types of motion—linear, circular, and oscillatory.

## Key Topics Covered

### 1. Understanding Measurement
- **Non-Standard Units**: Initially, people used body parts like handspans, arms, or feet to measure length. These are called non-standard units.
- **Problem with Non-Standard Units**: Such measurements varied from person to person.
- **Standard Unit Need**: To avoid confusion, standard units were introduced.

### 2. Standard Units of Length
- **SI Units**: The International System of Units (SI) provides standard measurements.
- **Base Unit**: Metre (m) is the SI unit of length.
- **Sub-units**:
- 1 kilometre (km) = 1000 metres (m)
- 1 metre = 100 centimetres (cm)
- 1 centimetre = 10 millimetres (mm)

- **Inches and Feet**: Older systems like inches and feet are still used in some places. 1 inch = 2.54 cm.

### 3. Correct Way to Measure Length
- **Selecting Proper Tool**: Use short scale (15 cm) for small objects and metre scale or measuring tape for larger ones.
- **Position of Scale**: The scale must be placed properly aligned with the object.
- **Eye Position**: The eye should be directly above the mark to avoid error.
- **Broken Scales**: Start from any visible mark and subtract the initial value from the final reading.
- **Visually Challenged Tools**: Special scales with raised markings help visually impaired students.

### 4. Measuring Curved Lines
- Use a **flexible tape** or **thread** to follow the curved path, then measure the thread with a scale.

### 5. Describing Position
- **Reference Point**: To describe a location accurately, a fixed point (reference point) is necessary.
- Example: Kilometre stones show how far you are from a city.
- **Position Change with Time**: If the distance from the reference point changes with time, the object is in motion.

### 6. Motion and Rest
- **Object in Motion**: Changes position over time with respect to reference point.
- **Object at Rest**: Position remains unchanged with respect to reference point.
- **Relative Motion**: Whether something is at rest or moving can depend on what you're comparing it to.

### 7. Types of Motion
- **Linear Motion**: Movement in a straight line (e.g., car on a straight road).
- **Circular Motion**: Movement in a circular path (e.g., merry-go-round).
- **Oscillatory Motion**: Back and forth movement (e.g., swing, pendulum).
- **Periodic Motion**: Motion that repeats at regular intervals (both circular and oscillatory motions are periodic).

---

## New Terms and Definitions

| Term | Simple Definition |
|-------------------|-------------------------------------------------------------------|
| Handspan | The distance from the tip of the thumb to the tip of the little finger |
| SI Units | International system used for standard measurement |
| Metre (m) | Standard unit for measuring length |
| Reference Point | A fixed point used to describe position or movement |
| Linear Motion | Motion in a straight line |
| Circular Motion | Motion in a circular path |
| Oscillatory Motion| Motion that moves back and forth |
| Millimetre (mm) | One-tenth of a centimetre |
| Kilometre (km) | A large unit for measuring long distances (1000 metres) |
| Periodic Motion | Motion that repeats after equal intervals of time |

---

## Practice Questions

### Easy (3)
1. **What is the SI unit of length?**
- **Answer**: Metre
- **Explanation**: The metre (m) is the standard SI unit used for measuring length.

2. **How many centimetres are there in 1 metre?**
- **Answer**: 100 cm
- **Explanation**: 1 metre = 100 centimetres.

3. **Which unit is suitable to measure the thickness of a page?**
- **Answer**: Millimetre
- **Explanation**: Pages are very thin, so mm is the most suitable small unit.

### Medium (2)
4. **Why can’t we use handspan to measure accurately?**
- **Answer**: Because handspans vary from person to person.
- **Explanation**: Handspan is a non-standard unit, and leads to inconsistent results.

5. **What is a reference point and why is it important?**
- **Answer**: A fixed point used to describe position.
- **Explanation**: It helps in determining whether something has moved or not.

### Difficult (3)
6. **Explain how to measure a curved line using a thread.**
- **Answer**: Place the thread along the curve, then straighten it and measure with a scale.
- **Explanation**: Threads can bend along the path and then be straightened for measurement.

7. **Differentiate between circular and oscillatory motion with examples.**
- **Answer**: Circular motion moves in a round path (e.g., fan), oscillatory moves to and fro (e.g., swing).
- **Explanation**: The paths and types of movements differ between these motions.

8. **A boy walks 2.5 km every day to school. How many metres does he walk?**
- **Answer**: 2500 metres
- **Explanation**: 1 km = 1000 m, so 2.5 × 1000 = 2500 m.

### Very Difficult (2)
9. **A scale has its zero mark broken. You measure a pencil from 1.2 cm to 8.6 cm. What is its length?**
- **Answer**: 7.4 cm
- **Explanation**: Subtract the lower reading from the upper: 8.6 - 1.2 = 7.4 cm.

10. **Why is it that passengers in a moving bus appear at rest to one another but in motion to a person standing outside?**
- **Answer**: Because motion is relative to the observer’s reference point.
- **Explanation**: Inside the bus, everyone has the same reference point, but outside, the bus is moving with respect to buildings and roads.

---