1.0 Lesson Objectives

• Scalars and Vectors
• Measurement Techniques
• Units and Symbols

1.1 Scalars and Vectors

·  Scalar Quantity

• A quantity that only has a magnitude
  • In simple terms we know how big or small it is, that is all. For example, a certain good has a mass of 100 kg. That is a static value, with no direction.
    • Mass is scalar
    • Other examples are time, length, mass, distance and speed.
    • SPEED DOES NOT HAVE A DIRECTION
      • Velocity does
      • Remember the difference
    • Similarly, distance is a generic quantity, without direction
      • When you add direction to it, it becomes displacement
        • Displacement is vector quantity

·  Vector Quantities

• It has both magnitude and direction
• Generally, many scalar quantities form a vector quantity when you add a direction to it.
• We know the size and the direction it goes towards
  • For example displacement means, in simplest terms, the distance a thing travels in a particular direction
  • If a person starts from his home in the morning, travels during the day to his office which is 10 km away, then comes back in the evening to his home again by traveling 10 km
    • His total displacement is zero by the end of the day (HE REACHED BACK WHERE HE STARTED, so he did not cover any distance in a particular direction)
    • However, the total distance, a scalar quantity, that he traveled, is 20 km (10 to office and 10 back from office)
  • Other examples are velocity (speed in a particular direction), force (like weight), acceleration etc.

Resultant of two vectors

·  Head to tail rule

• Head is the part of the vector with arrow
• Tail is the side without it
• Connect the head of one vector A to the tail of Vector B, then measure the length of the line between tail of Vector A to head of Vector B
• In exams
  • Either just point out of resultants is required
  • OR you are required to apply simple trigonometry
    • E. sin, cos, tan

·  Parallelogram Rule

• A little complicated
• You need to complete the parallelogram (we will do questions of these in past paper discussion class to clarify
• Then, take measurement of the diagonal
  • Will do it past paper class to demonstrate as well

1.2 Measurement Techniques

Rules

• If the length is very short, for example if the diameter of a small wire is to be measured, we use micrometer screw gauge
  • The reason is that it can give answer accurate to 0.01 mm
    • So limits of accuracy are 0.005mm + and –

·  If we have short length

• Measuring cylinder’s diameter
• Vernier Calipers are used
• Accurate to 0.01 cm
  • Limits of accuracy would be 0.005 cm + and –

·  For lengths that are medium

• Image distance in lens
• Metre rule (the ruler we use in our exams)
• Accuracy is 0.1 cm
  • Limits of accuracy are 0.05cm + and –

Vernier Caliper

·   It has two jaws

• Inner one is used for internal diameter (for example if you have scotch tape and you want to measure the diameter of the inner part, we use inner jaw)
• Outer jaw is for external diameter, for example the diameter outside the tape

·   The item is placed in between the jaw that is to be measured

• Tighten the jaw until the item is firm
• Not too hard so that the item is not compressed
• Do not leave it loose or the measurement is incorrect

·   How to read

• First, check the reading that is before the zero marking
  • The marking that shows first decimal place
• Then, for the second decimal place
  • See where the vernier scale is adjacent to the main scale
• Add the two readings to get the complete answer.

·   Before starting your measurement

• You need to check for zero error
  • Make both jaws of the caliper equal
  • If when this happens, the scales do not have the same value, then there is a zero error in the caliper.
• We have to add or subtract this change in value to our final answer

Micrometer Screw Gauge

·   We use the thimble to control the gauge

• Turning the thimble until the spindle and anvil will have proper grip of our object
• DO NOT MAKE IT TOO TIGHT
• First read the main scale, that gives us the first value
• Then, check which number of the circular scale is in line with the main scale number we just saw (there is a horizontal line there)
• That is the value of our reading.
• The first reading is the first decimal place
• The second is the second decimal place
• Add them and you get the final answer

·   We will attempt questions in paper discussion class – so that understanding is easier

• Usually in paper 1, you are asked to read the reading from instruments and choose the right answer
• In ATP, you may be required to read the readings and put the value.

Pendulum

• There is a bob (the end part) and the string (that holds the end part)

·   Oscillation

• One complete round movement. If the start point is the middle position and we call it X
• If we call the left extreme height Y and Right complete height Z
• Then Oscillation is X to Y to Z to X
  • OR X to Z to Y to X
• Remember, oscillation completes when the bob returns to the mean position after reaching both side heights

·   Period

• Symbol is T
• Time taken for one complete oscillation (Movement)
• Frequency
  • Complete oscillations made per second
  • Oscillation/Time
  • For example, if a pendulum makes 100 oscillations in 10 seconds
    • 100/10
    • Frequency is 10 hertz (will study the measurements)

·   Pendulum Period (time taken for one oscillation) is affected by

• Length of the string
  • The longer the string, the longer the period
• Acceleration
  • Gravitational pull on the pendulum
  • The higher the gravitational pull, the shorter the period

·   How to measure period

• Use stopwatch
• Take the time that the pendulum takes for a larger number of oscillations, say 30 oscillations
• Divide the total time by number of oscillations, so we get the time taken by one oscillation
• That becomes our period
• So Period = Time taken total/ Number of oscillations

Time Measurement

·   Intervals can be different in measurement

• For example one measurement may note the seconds, while other may note decades
• Radioactive Decay clocks
  • It measures the age of excavated ancient material
• Pendulum clock
  • Used for hours, minutes and seconds measurements in longer intervals
• A regular wrist watch
  • Longer time intervals – same as pendulum clock
• Ticker-tape timer
  • 02 seconds interval
• Analogue stopwatch
  • The accuracy here is 0.1 s + and –
  • So small time intervals in minutes and seconds
• Digital Stopwatch
  • Even more accurate as the accuracy is 0.01s
• Atomic clock
  • The most accurate
  • Time interval is 10-10

Main types of Errors that occur in measurement

·   Zero error

• Error of equipment
• When a CLOSED equipment gives something higher of lower than zero as a reading
• So we add the number to the final result if it was initially giving lower than zero
• We subtract the number if it was initially higher than zero

·   Parallax error

• Human positioning
  • Your eye level is not correctly on the reading point
  • Eyes must be PERPENDICULAR (90 degree angle) to the point of reading for accurate reading

·   Human Reaction Error

• Human error
  • Time intervals being taken wrong due to reaction time issue
  • For example, a person is running in a race and I am timing.
  • When the person reaches finish line, I take 1 second extra to stop the stopwatch than the actual end time
  • Either we should take repeated values (reliability) and take average
  • OR use computerized equipment instead to avoid this error

Some Precautions when using equipment

• Make sure you check for zero error
  • Add or subtract value
  • Parallax error must be avoided
  • Your grip must be gentle, not too tight
  • Reliability improves by taking repeat measurements and taking average
  • Instruments should be cleaned and wiped to remove any dust or any other thing hindering correct measurement or reading

Measuring Tape

• Plastic Strip
• Many meters in length
• Usually in feet, inch, meters, cm, mm etc
• 1 mm or 0.1 cm accuracy
• Distance between two points is measured
• Also used to measure diameter and circumference of curved objects

 

Meter Rule

• Ruler (wood, plastic, steel)
• 1 m or 100 cm length total
• Measures in mm, cm and inches
• Accuracy is 10 mm or 0.1 cm
• Straight distance and objects measured
• Have to avoid parallax error
• Instrument can get damaged by wear and tear
  • Reading can become difficult
  • Result in zero error

1.3 Measurement SI Units

• Remember, our focus is to ensure that our measurements are final in these aspects
  • We will generally report answers in these until otherwise stated

 

Name of Quantity	SI Unit	Symbol
Mass	Kilogram	Kg
Time	Second	s
Current	Ampere	A
Length	Metre	m
Light Intensity	Candela	Cd
Substance amount	Mole	Mol
Temperature	Kelvin	K

The Generally accepted prefixes for SI Units These help to show large quantities and values in smaller writings

Prefix Name	Value	Symbol
Deci		d
Centi		c
Milli		m
Micro
Nano		n
Kilo		K
Mega		M
Giga		G