Measurement of Length and Motion

How Do We Measure Length?

• Our Experience:
  • When we want to buy a new tablecloth, so we sometimes measure the length with our handspan. But if we measure using hand span, then the results can be different for different people. This can lead to confusion and thus the need for a proper way to measure length arises.

Need for Standard Units

• Why Handspan Isn’t Accurate:
  • Using different people’s handspan, foot length, or arm length can give different measurements. This is because different people have different sizes of body parts.
  • Example: Your handspan might be smaller than your elder brother’s, causing measurements of the same object to be different.
• Standard Units:
  • To avoid confusion, scientists developed standard units that are the same everywhere. This ensures that everyone gets the same measurement, no matter who is measuring or where it is done.
  • People use rulers and measuring tapes for standard measurement.
  • Body-part measurements differ, so we need standard units for accuracy.

What is Measurement?

• Definition: Measurement is the process of comparing an unknown quantity with a known fixed quantity called a unit.
  • Example: If you say the length of a pencil is 15 cm, the unit you are using is centimeters (cm), and 15 is the number of these units.
  • Thus the length of something is expressed in two parts: a number and a unit (like 13 cm).

1. Historical Methods of Measurement:

• Ancient Methods: Before standard units, people used body parts to measure things. This included:
  • Cubit: The distance from the elbow to the tip of the middle finger.
  • Handspan: The distance between the tip of the thumb and the little finger when the hand is fully extended.
  • Foot: The length of a person’s foot.
  • Ancient Indian units like “angula” (finger width), “dhanusa,” and “yojana” were also used.
  • Craftsmen like carpenters still use “angula” for measurement.
  • Even in ancient times, people used scales to measure.
• Why Ancient Methods Were Problematic: Different people have different-sized feet, hands, and arms, so these methods led to inaccuracies.

2. Standard Methods/Units of Measurement of Length:

• Unit: The basic unit of length is the meter (m).
  • Conversions:
    • 1 meter (m) = 100 centimeters (cm)
    • 1 centimeter (cm) = 10 millimeters (mm)
    • 1 kilometer (km) = 1000 meters (m)
• Tools for Measuring Length:
  • Meter scale: Used to measure larger objects like a table or the height of a person.
  • Measuring tape: Useful for measuring longer distances or round objects.
  • Ruler: Usually 15 cm or 30 cm long, used for small objects like a book or a pencil.

International System of Units (SI):

• SI Unit of Length: Meter (m) is the internationally accepted unit for measuring length.
• Other common SI units used for length:
  • Centimeter (cm): Used for small lengths like the width of a notebook.
  • Kilometer (km): Used for longer distances like the distance between two cities.

How to Measure Length Accurately

• Using a Scale Correctly:

• When measuring with a scale, it is important to place the scale along the object carefully.
• Steps for Correct Measurement:
  • Ensure the scale is aligned properly with the object.
  • Keep your eye directly above the object when reading the measurement. If you look from an angle, the measurement may appear different, which can cause errors.
  • Start measuring from the zero mark on the scale to avoid mistakes.

• Handling a Broken Scale:
  • If the scale’s zero mark is damaged or unclear, you can start measuring from any other mark (e.g., from 1 cm). To get the correct length, subtract the starting mark from the ending mark.
  • Example: If your scale is broken and starts from the 5 cm mark to the 15 cm mark, the length of the object is 15 – 5 = 10 cm.

Measuring Curved Lines

• Measuring with a Thread:
• Straight objects are easy to measure with a scale, but measuring curved lines is more difficult.
• Steps to Measure a Curved Line:
  • Place a thread along the curved path.
  • Mark the endpoints of the curve on the thread.
  • Stretch the thread straight and measure its length using a meter scale or ruler.

Describing Position

• Reference Point: A fixed point used to measure distances. It helps make distance comparisons consistent.
• Example:
  • Students debated the distance between the garden and the school.
  • Their answers differed because they measured from their houses. Using a common point (like a bus stand) would give the same result for all.
• Kilometer Stones: Show the distance from a place, using that place as the reference point (e.g., “Delhi 70 km”).
• Conclusion: A reference point is necessary to accurately describe and compare positions and distances.

Moving Objects Around Us

• We observe many objects moving or staying at rest around us.
• Examples of Objects at Rest:
  • A table, a chair, a wall.
• Examples of Objects in Motion:
  • A bird flying, a car moving, a clock’s hands.

What is Motion?

• Definition: Motion is the change in the position of an object over time.
• Or If an object changes its position with time relative to a reference point, it’s in motion. & If it doesn’t change position, it’s at rest.

Examples of Motion:

• A ball rolling across the floor moves from one point to another.
• The hands of a clock rotate, changing their position continuously.

Types of Motion

1. Linear or Rectilinear Motion:

• Definition: Motion in a straight line.
• Examples:
  • A car driving on a straight road.
  • A sprinter running in a 100-meter race.
  • A stone falling vertically down.
  • An orange falling from a tree,
  • Students marching in a parade.

2. Circular Motion:

• Definition: Motion along a circular path around a fixed point.
• Examples:
  • The hands of a clock moving around the dial.
  • The blades of a fan spinning around the center.
  • Whirling an eraser on a string.
  • A merry-go-round.

3. Oscillatory Motion:

• Definition: When an object moves back and forth.
• Examples:
  • A swing.
  • A hanging eraser moving side to side like a pendulum.
  • Pressing and releasing a metal strip (vibrating metal strip).

4. Periodic Motion:

• Definition: Motion that repeats itself after a fixed period of time.
• Examples:
  • The pendulum of a clock swinging back and forth.
  • A child on a swing going up and down.

Combination of Motions

• Sometimes, an object may exhibit more than one type of motion at the same time.
• Example: A rolling ball moves in a straight line (linear motion) while also spinning (rotational motion).
• Real-Life Examples:
  • The Earth rotates on its axis (rotational motion) and revolves around the Sun (circular motion).

Chapter Summary:

• Measurement helps us compare and understand the size and distance of objects.
• Standard units like meters and centimeters are used globally to ensure consistency.
• Motion is the change in position of an object, and objects can show different types of motion like rectilinear, circular, and periodic.

Important Terms:

• Motion: The change in the position of an object over time.
• Measurement: Comparing an unknown quantity with a known standard unit.
• Rectilinear Motion: Motion in a straight line.
• Circular Motion: Motion along a circular path.
• Periodic Motion: Motion that repeats at regular intervals.