Length and Time
Physics / General Physics / BGCSE Single Science
Learning Objective
Explain what fundamental physical quantities are and state their corresponding SI units
Introduction: Why Length and Time Matter in Physics
All physical measurements in science are built upon a small number of fundamental physical quantities. Among the most important and commonly used of these are length and time.
In everyday life, we constantly measure:
- The length of a road, a classroom, or a wire
- The time taken to walk to school, cook food, or complete an exam
In physics, however, measurements must be:
- Standardised
- Precise
- Universally accepted
This is achieved by using fundamental quantities measured in SI units. A clear understanding of these quantities is essential for success in:
- Calculations
- Experiments
- Data interpretation
- All physics topics that follow
Fundamental Physical Quantities
Meaning of a Fundamental Physical Quantity
A fundamental physical quantity is a physical quantity that:
- Can be measured directly
- Does not depend on any other physical quantity
- Forms the foundation for defining all other quantities
Derived quantities such as speed, density, force, and energy are calculated using fundamental quantities.
Fundamental Physical Quantities in Physics
At BGCSE level, the most important fundamental physical quantities include:
- Length
- Mass
- Time
- Electric current
- Temperature
In this subtopic, the focus is on length and time.
Length
Definition of Length
Length is the measure of the distance between two points.
It is used to measure:
- Height
- Width
- Thickness
- Distance
- Diameter
SI Unit of Length
The SI unit of length is the metre (m). The metre is an internationally agreed standard, ensuring that measurements taken in Botswana are the same as those taken anywhere else in the world.
Common Units of Length
Although the metre is the SI unit, other units are commonly used depending on the size of the object being measured:
| Unit | Symbol | Relationship to metre |
|---|---|---|
| kilometre | km | 1 km = 1000 m |
| centimetre | cm | 1 cm = 0.01 m |
| millimetre | mm | 1 mm = 0.001 m |
Measuring Length in Practice
Length is measured using instruments such as:
- Metre rule
- Tape measure
- Vernier calipers
- Micrometer screw gauge
Each instrument is chosen based on the required accuracy.
Time
Definition of Time
Time is the measure of the duration of an event or the interval between two events.
Examples include:
- Time taken for a pendulum to complete one swing
- Time taken for a car to travel a certain distance
- Time interval between two lightning flashes
SI Unit of Time
The SI unit of time is the second (s). The second is defined using highly precise atomic standards, making it extremely accurate and reliable.
Common Units of Time
In daily life and experiments, other time units may be used:
| Unit | Symbol | Relationship to second |
|---|---|---|
| millisecond | ms | 1 ms = 0.001 s |
| minute | min | 1 min = 60 s |
| hour | h | 1 h = 3600 s |
Measuring Time in Practice
Time is measured using:
- Stopwatch
- Digital timer
- Clock
- Electronic sensors (in advanced experiments)
Accuracy depends on:
- Reaction time of the observer
- Precision of the instrument used
Importance of SI Units in Physics
Using SI units ensures that:
- Measurements are consistent
- Calculations are correct
- Results can be compared internationally
- Scientific communication is clear and unambiguous
In examinations, failure to use SI units correctly can result in loss of marks, even if the method is correct.
Practice Questions
Question 1 (AO1)
State two fundamental physical quantities and give their SI units.
Two fundamental physical quantities are:
- Length — SI unit: metre (m)
- Time — SI unit: second (s)
Question 2 (AO1)
Which of the following is the SI unit of length?
A. centimetre B. millimetre C. metre D. kilometre
Correct answer: C — metre
The metre is the internationally accepted SI base unit for length.
Question 3 (AO2)
A student records the length of a wire as 250 cm. Convert this length into metres.
Given: Length = 250 cm
Conversion: 1 m = 100 cm
250 ÷ 100 = 2.5 m
Question 4 (AO1)
State the SI unit of time and name one instrument used to measure it.
The SI unit of time is the second (s).
One instrument used to measure time is a stopwatch.
Question 5 (AO2 – Thinking Skill)
Explain why the metre is preferred over the centimetre when recording scientific measurements.
The metre is preferred because:
- It is the SI base unit
- It reduces the need for frequent conversions
- It improves clarity and standardisation in scientific work
- It minimises calculation errors
Learning Objective
Use a metre rule, vernier calipers, and a micrometer screw gauge to measure small lengths correctly
Introduction: Accuracy in Measuring Small Lengths
In physics, many quantities are very small and cannot be measured accurately using ordinary methods. Examples include:
- Thickness of a wire
- Diameter of a small rod
- Thickness of a sheet of paper
- Internal diameter of a tube
Accurate measurement of such small lengths requires:
- Appropriate measuring instruments
- Correct reading techniques
- Awareness of instrument limitations
- Careful handling to minimise errors
This skill is essential for:
- Practical work
- Alternative to Practical questions
- Data interpretation
- Reliable scientific conclusions
Measuring Length Using a Ruler
Description of a Ruler
A ruler (or metre rule) is the simplest instrument used to measure length. It usually has:
- A scale graduated in millimetres (mm) and centimetres (cm)
- A least count of 1 mm
Correct Method of Using a Ruler
To measure length accurately using a ruler:
- Place the object in contact with the ruler.
- Align one end of the object with the zero mark.
- Read the scale at the other end of the object.
- Ensure your eye is directly above the scale to avoid parallax error.
Limitations of a Ruler
- Not suitable for very small measurements
- Zero mark may be worn or damaged
- Accuracy limited to ±1 mm
For higher precision, more sensitive instruments are required.
Vernier Calipers
Description of Vernier Calipers
Vernier calipers are used to measure:
- External diameter
- Internal diameter
- Depth of objects
They consist of:
- A main scale
- A vernier scale
- Fixed and movable jaws
- A depth rod
Least Count of Vernier Calipers
The least count is the smallest length that can be measured accurately.
For a standard vernier caliper: Least count = 0.1 mm or 0.01 cm
Steps to Read Vernier Calipers
- Close the jaws gently around the object.
- Read the main scale reading just before the zero of the vernier scale.
- Identify the vernier scale division that aligns exactly with a main scale mark.
- Multiply the aligned division by the least count.
- Add this value to the main scale reading.
Total reading = Main scale reading + Vernier scale reading
Advantages of Vernier Calipers
- Greater accuracy than a ruler
- Measures internal and external dimensions
- Suitable for laboratory and exam situations
Micrometer Screw Gauge
Description of a Micrometer Screw Gauge
A micrometer screw gauge is used to measure very small lengths, such as:
- Thickness of a wire
- Thickness of paper
- Diameter of small spheres
It consists of:
- Anvil
- Spindle
- Sleeve (main scale)
- Thimble (rotating scale)
- Ratchet
Least Count of a Micrometer Screw Gauge
- Typical least count = 0.01 mm
- This makes it more accurate than vernier calipers
Steps to Read a Micrometer Screw Gauge
- Place the object between the anvil and spindle.
- Turn the ratchet until a clicking sound is heard.
- Read the sleeve (main scale) reading.
- Read the thimble scale reading.
- Add both readings.
Total reading = Sleeve reading + Thimble reading
Importance of the Ratchet
The ratchet ensures:
- Uniform pressure
- Prevention of damage to the instrument
- More reliable readings
Sources of Error in Measuring Small Lengths
Common errors include:
- Parallax error (eye not perpendicular to scale)
- Zero error (instrument does not read zero when closed)
- Excessive force applied
- Worn or damaged instruments
Students must always:
- Check for zero error
- Apply corrections where necessary
Practice Questions
Question 1 (AO1)
Name one instrument suitable for measuring the thickness of a wire and state its least count.
A micrometer screw gauge is suitable.
Least count = 0.01 mm.
Question 2 (AO2)
Explain why a ruler is not suitable for measuring the diameter of a thin wire.
A ruler is not suitable because:
- Its least count is large (1 mm)
- The wire diameter is very small
- This leads to large percentage error
Question 3 (AO3)
State two precautions taken when using a vernier caliper to ensure accurate measurements.
Precautions include:
- Ensuring jaws are clean
- Avoiding excessive pressure
- Reading scales at eye level
- Checking for zero error
Question 4 (AO2)
A micrometer screw gauge has a sleeve reading of 2.50 mm and a thimble reading of 0.28 mm. Calculate the thickness of the object.
Given:
- Sleeve reading = 2.50 mm
- Thimble reading = 0.28 mm
Thickness = 2.50 + 0.28 = 2.78 mm
Question 5 (AO3 – Higher Order)
Suggest two ways of improving the accuracy when measuring very small lengths in the laboratory.
Accuracy can be improved by:
- Using a micrometer instead of a ruler
- Taking repeated readings and averaging
- Avoiding parallax error
- Applying zero error corrections
Learning Objective
Describe common sources of error when measuring length with different instruments
Introduction: Why Errors Occur in Measurements
No measurement in physics is perfectly exact. Even when using correct instruments, measurements may differ slightly from the true value due to errors.
Understanding sources of error is essential because it enables students to:
- Judge the reliability of measurements
- Improve experimental techniques
- Interpret results correctly
- Score well in Alternative to Practical and theory questions
Meaning of Measurement Error
A measurement error is the difference between the measured value and the true or accepted value of a quantity.
Errors do not necessarily mean a mistake has been made; they are a natural part of measurement.
Types of Errors in Measuring Length
When measuring length, errors generally fall into the following categories:
- Instrumental errors
- Observational errors
- Procedural errors
Zero Error
Description of Zero Error
Zero error occurs when a measuring instrument does not read zero when it should. For example:
- A ruler with a worn or broken zero mark
- Vernier calipers whose jaws do not align at zero
- A micrometer screw gauge that shows a reading when fully closed
Effect of Zero Error
- All readings taken will be systematically incorrect
- The error affects every measurement in the same way
- Results may be consistently higher or lower than the true value
Parallax Error
Description of Parallax Error
Parallax error occurs when the observer's eye is not positioned directly above the scale while taking a reading. This causes the scale reading to appear shifted.
Effect of Parallax Error
- Reading may be too large or too small
- Error varies depending on viewing angle
- Common when using rulers and vernier calipers
Instrument Resolution (Least Count Error)
The least count of an instrument is the smallest length it can measure accurately. For example:
| Instrument | Least Count |
|---|---|
| Ruler | 1 mm |
| Vernier calipers | 0.1 mm |
| Micrometer screw gauge | 0.01 mm |
Effect on Measurement
- Instruments with a large least count give less precise measurements
- Small objects measured with low-resolution instruments produce large percentage errors
Misalignment Error
Misalignment occurs when:
- The object is not placed parallel to the scale
- The object is tilted or skewed during measurement
Effect: Length measured may be longer or shorter than the true value. Common when measuring long or flexible objects.
Excessive Force or Pressure
Applying too much force when using vernier calipers or micrometer screw gauges can compress the object or distort the instrument.
Effect: Results in readings smaller than the true value. Particularly significant when measuring soft materials.
Worn or Damaged Instrument
Instruments may be old, bent, or have faded or unclear markings.
Effect: Readings become unreliable and it becomes difficult to identify exact scale divisions.
Practice Questions
Question 1 (AO1)
What is meant by zero error in the measurement of length?
Zero error occurs when a measuring instrument does not read zero when it should, causing all measurements to be consistently incorrect.
Question 2 (AO2)
A ruler has its zero mark worn away. Identify the source of error and explain how it affects measurements.
The source of error is zero error due to a damaged zero mark.
This causes all readings to be either larger or smaller than the true value.
Question 3 (AO3)
From a given diagram of a student reading a ruler from the side, identify the error and name it.
The error is parallax error, caused by incorrect eye position while reading the scale.
Question 4 (AO2)
Explain why a ruler introduces greater measurement error when measuring the thickness of a wire.
A ruler has a large least count (1 mm). When measuring a thin wire, this causes a large percentage error, reducing accuracy.
Question 5 (AO3 – Higher Order)
State two precautions that reduce errors when measuring length using a micrometer screw gauge.
Precautions include:
- Using the ratchet to apply uniform pressure
- Checking for zero error before measurement
- Taking repeated readings and averaging
- Reading scales at eye level
Learning Objective
Measure time intervals accurately using a stopwatch or stop clock
Introduction: Importance of Accurate Time Measurement
Time measurement is fundamental in physics because many quantities depend directly on time, such as:
- Speed
- Acceleration
- Frequency
- Period of oscillation
Inaccurate time measurement leads to:
- Incorrect calculations
- Unreliable experimental results
- Wrong scientific conclusions
Instruments Used to Measure Time
Stop Clock
A stop clock is a timing device designed to measure short time intervals accurately. Types include:
- Analogue stop clock
- Digital stop clock
Watch or Clock
A watch or wall clock may be used for:
- Longer time intervals
- Everyday measurements
- Situations where high precision is not required
Least Count of Time-Measuring Instruments
The least count of a time-measuring instrument is the smallest time interval it can measure accurately. Typical values:
| Instrument | Least Count |
|---|---|
| Analogue stop clock | 0.1 s |
| Digital stop clock | 0.01 s |
| Watch | 1 s |
The smaller the least count, the higher the accuracy.
Correct Procedure for Measuring Time Using a Stop Clock
To measure time accurately using a stop clock:
- Reset the stop clock to zero.
- Position yourself so the display is clearly visible.
- Start the stop clock at the exact beginning of the event.
- Stop the clock at the exact end of the event.
- Record the time shown.
Measuring Short Time Intervals Accurately
Reaction Time Error
Human reaction time introduces error when starting and stopping the clock. This error is significant for very short time intervals.
Reducing Reaction Time Error
Accuracy can be improved by:
- Measuring longer time intervals
- Timing several cycles of an event
- Dividing total time by number of cycles
Example: Time 20 oscillations of a pendulum, then divide by 20 to find time for one oscillation.
Common Errors in Measuring Time
Sources of error include:
- Reaction time delay
- Failure to reset the clock
- Parallax error when reading analogue clocks
- Low instrument resolution
- Inconsistent start and stop points
Practice Questions
Question 1 (AO1)
Name one instrument used to measure time in physics and state its least count.
A digital stop clock is used to measure time.
Its least count is 0.01 s.
Question 2 (AO2)
Explain why timing several oscillations of a pendulum gives more accurate results than timing one oscillation.
Timing several oscillations reduces the effect of reaction time error because the reaction delay becomes a smaller fraction of the total time measured.
Question 3 (AO3)
State two precautions taken when measuring time using a digital stop clock.
Precautions include:
- Resetting the stop clock before use
- Ensuring clear visibility of the display
- Starting and stopping at consistent reference points
- Avoiding parallax error on analogue clocks
Question 4 (AO2)
A student records a time of 40.0 s for 20 oscillations of a pendulum. Calculate the time for one oscillation.
Given: Total time = 40.0 s, Number of oscillations = 20
Time for one oscillation = 40.0 ÷ 20 = 2.0 s
Question 5 (AO3 – Higher Order)
Identify two sources of error when measuring short time intervals and suggest how each error can be reduced.
Sources of error and reductions:
- Reaction time error: time many cycles and average
- Instrument resolution error: use a digital stop clock with smaller least count
Learning Objective
Judge the precision and accuracy of measuring instruments used for time and length
Introduction: Why Estimating Accuracy Matters
In physics, obtaining a measurement is not enough. A scientist must also be able to judge how accurate that measurement is.
Estimating accuracy allows students to:
- Decide whether an instrument is suitable for a task
- Compare different measuring instruments
- Evaluate the reliability of experimental results
- Justify choices made during practical work
Meaning of Accuracy in Measurement
Accuracy refers to how close a measured value is to the true or accepted value.
An accurate measurement:
- Has a small error
- Uses an appropriate instrument
- Is recorded correctly with suitable units
Accuracy is different from precision:
- Accuracy: closeness to the true value
- Precision: repeatability of measurements
Factors That Determine the Accuracy of a Measuring Instrument
The accuracy of a measuring instrument depends on several key factors:
- Least count (resolution)
- Condition of the instrument
- Presence of zero error
- Method of use
Least Count and Accuracy
Meaning of Least Count
The least count is the smallest measurement that an instrument can record reliably. Examples:
| Instrument | Least Count |
|---|---|
| Ruler | 1 mm |
| Vernier calipers | 0.1 mm |
| Micrometer screw gauge | 0.01 mm |
| Digital stop clock | 0.01 s |
Relationship Between Least Count and Accuracy
- Smaller least count → higher accuracy
- Larger least count → lower accuracy
An instrument cannot measure more accurately than its least count.
Estimating Accuracy from Least Count
Estimated accuracy ≈ ±½ of the least count
Examples:
- Ruler (1 mm): accuracy ≈ ±0.5 mm
- Vernier calipers (0.1 mm): accuracy ≈ ±0.05 mm
Condition of the Instrument
Instruments that are old, bent, worn, or have faded markings produce measurements with reduced accuracy.
Accuracy is reduced if:
- Zero mark is damaged
- Scale divisions are unclear
- Moving parts do not move smoothly
Zero Error and Accuracy
Zero error directly affects accuracy.
- If zero error is present, accuracy decreases
- If zero error is corrected, accuracy improves
Method of Use
Even a highly accurate instrument can give poor results if used incorrectly. Accuracy is reduced by:
- Parallax error
- Misalignment of the object
- Excessive force
- Inconsistent reading technique
Practice Questions
Question 1 (AO1)
Define the term accuracy as used in physics measurements.
Accuracy is the closeness of a measured value to the true or accepted value.
Question 2 (AO2)
A ruler has a least count of 1 mm. Estimate the accuracy of the ruler.
Least count = 1 mm
Estimated accuracy = ±½ × 1 = ±0.5 mm
Question 3 (AO2)
State one reason why a micrometer screw gauge is more accurate than a vernier caliper.
A micrometer screw gauge has a smaller least count (0.01 mm), making it more accurate.
Question 4 (AO3)
A student uses a damaged ruler to measure the length of a book. Explain how this affects the accuracy of the measurement.
A damaged ruler produces unclear readings, increasing uncertainty and reducing measurement accuracy.
Question 5 (AO3 – Higher Order)
A student must measure the diameter of a thin wire. Which instrument should be used and why?
A micrometer screw gauge should be used because:
- The wire diameter is very small
- The micrometer has high accuracy
- Percentage error is minimised
Learning Objective
Identify typical errors involved in time measurements and explain how they can be reduced
Introduction: Why Time Measurement Is Prone to Error
Measuring time may appear simple, but it is one of the most error-prone measurements in physics. Unlike length, time measurement often depends on:
- Human response
- Clear identification of start and end points
- Instrument sensitivity
Understanding errors in time measurement allows students to:
- Improve accuracy
- Evaluate experimental data
- Explain anomalies in results
- Answer Alternative to Practical questions confidently
Meaning of Error in Time Measurement
An error in time measurement is any factor that causes the recorded time to differ from the true duration of an event.
Errors may arise from:
- The observer
- The measuring instrument
- The method used
Reaction Time Error
Description
Reaction time error occurs due to the delay between observing the start or end of an event and pressing the start or stop button on a timing device. This delay is caused by the natural limitations of the human nervous system.
Effect on Measurement
- Measured time may be longer or shorter than the true value
- The error is significant for short time intervals
- Results vary between different observers
Identification
Reaction time error is present when:
- A stop clock is operated manually
- Short-duration events are timed
- Different readings are obtained by different students
Instrument Resolution (Least Count Error)
The least count of a time-measuring instrument is the smallest time interval it can measure accurately. Examples:
| Instrument | Least Count |
|---|---|
| Analogue stop clock | 0.1 s |
| Digital stop clock | 0.01 s |
| Watch | 1 s |
Effect on Accuracy
- Instruments with large least counts give less accurate results
- Small time intervals cannot be measured precisely with low-resolution instruments
Parallax Error (Analogue Clocks)
Parallax error occurs when the observer's eye is not positioned directly above the pointer of an analogue clock or stopwatch.
Effect:
- The time reading appears shifted
- Leads to incorrect start or stop readings
Zero Error in Timing Devices
Zero error occurs when a stop clock does not reset to zero before timing or has a faulty reset mechanism.
Effect:
- All recorded times are offset by a constant amount
- Accuracy of results is reduced
Inconsistent Start and Stop Points
Errors arise when the start of an event is not clearly defined or different criteria are used to start or stop timing. Examples:
- Timing a runner without a clear signal
- Timing oscillations without consistent reference points
Effect:
- Large variation in recorded times
- Poor repeatability of results
Fatigue and Loss of Concentration
When experiments are repeated many times, observer concentration may decrease and response time becomes inconsistent.
Effect:
- Increased random error
- Reduced reliability of data
Practice Questions
Question 1 (AO1)
What is reaction time error?
Reaction time error is the delay between observing an event and starting or stopping the timing device.
Question 2 (AO2)
Explain why reaction time error is more significant when measuring short time intervals.
For short intervals, reaction time forms a large fraction of the measured time, increasing percentage error.
Question 3 (AO3)
From a diagram showing a student reading an analogue stopwatch at an angle, identify the source of error.
The error is parallax error, caused by incorrect eye position when reading the scale.
Question 4 (AO2)
State two sources of error when measuring time using a stop clock.
Sources of error include:
- Reaction time delay
- Low instrument resolution
- Failure to reset the stop clock
- Parallax error on analogue devices
Question 5 (AO3 – Higher Order)
Suggest two methods of reducing errors when measuring the period of a pendulum.
Errors can be reduced by:
- Timing many oscillations and averaging
- Using a digital stop clock with a small least count
- Ensuring consistent start and stop points