Units and Measurement Lecture Notes

Introduction

• Welcome SBWB gang seniors
• Encouragement to engage (like, subscribe, share)
• Today's topic: Third part of Chapter on Units and Measurement

Previous Topics Recap

• Conversion between degrees and radians
• Parallax method for measuring distances of stars and planets
• Measurement of very small distances (atoms/molecules) using electron microscopes

New Topics Today

Key Concepts to Cover

1. Accuracy
2. Precision
3. Uncertainty in Measurements
4. Numericals related to Errors

Accuracy

• Definition: Closest value to the correct value (degree of closeness)
• Example: Actual length = 15 cm, measured = 14.95 cm (accurate)
• Importance of accuracy in measurements

Precision

• Definition: Degree of repeatability in measurements
• Example: If repeated measurements yield values close to each other, they are precise.
• Distinction from accuracy: Accuracy is about closeness to the true value, precision is about consistency of measurements.

Uncertainty

• Definition: Degree of sudden change; indicates how much a measured value can differ from the actual value.
• Example: Expected value = 15 cm, but measured = 2 cm (high uncertainty)
• Relation to errors in measurement.

Errors in Measurement

Types of Errors

1. Systematic Errors

   • Occur in one direction (positive or negative)
   • Causes:
     • Imperfection in technique
     • External factors (e.g., temperature, humidity)
     • Personal error (casual behavior during measurement)

2. Random Errors

   • Caused by unpredictable fluctuations in measurement
   • Cannot be associated with a constant cause
   • Example: Misreporting of an answer in calculations

Reducing Errors

• Observing and repeating measurements can reduce random errors.
• More observations lead to less random error.

Calculating Errors

Mean Error

• Formula: ( A_{mean} = \frac{A_1 + A_2 + A_3 + A_n}{n} )
• Example
  • Given values: 20 cm, 21 cm, 22.5 cm, 26.5 cm
  • Mean calculation: 90 cm / 4 = 22.5 cm_

Mean Absolute Error

• Formula: ( \Delta A_{mean} = \frac{\text{sum of } |A_{mean} - A_i|}{n} )
• Example calculated with previous values leading to an average absolute error.

Relative Error

• Formula: ( \frac{\Delta A_{mean}}{A_{mean}} )
  • Expressed as a fraction of the mean value.

Percentage Error

• Multiply relative error by 100 to express it as a percentage.

Homework and Practice

• Review errors and calculations in the textbook.
• Prepare for upcoming chapters and ensure understanding of dimensions.

Conclusion

• End of chapter discussion
• Encouragement to review and engage with materials provided on Telegram.
• Next chapter will start tomorrow.
• Focus on learning dimensions in upcoming classes.