Different types of vectors.

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1.4 Scalars and Vectors
• Scalar quantities are quantities that have
magnitude only. Two examples are shown below:
Measuring Mass Measuring Temperature

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1.4 Scalars and Vectors
• Scalar quantities are added or subtracted by using
simple arithmetic.
Example: 4 kg plus 6 kg gives the answer 10 kg
+ =
4 kg
6 kg
10 kg

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1.4 Scalars and Vectors
• Vector quantities are quantities that have both
magnitude and direction
Magnitude = 100 N
Direction = Left
A Force

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1.4 Scalars and Vectors
• Examples of scalars and vectors
Scalars Vectors
distance displacement
speed velocity
mass weight
time acceleration
pressure force
energy momentum
volume
density

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1.4 Scalars and Vectors
Adding Vectors using Graphical Method
• Parallel vectors can be added arithmetically
2 N
4 N
6 N 4 N
2 N
2 N

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1.4 Scalars and Vectors
Adding Vectors using Graphical Method
• Non-parallel vectors are added by graphical
means using the parallelogram law
– Vectors can be represented graphically by arrows
– The length of the arrow represents the magnitude of the
vector
– The direction of the arrow represents the direction of the
vector
– The magnitude and direction of the resultant vector can be
found using an accurate scale drawing
5.0 cm  20.0 N
Direction = right

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• The parallelogram law of vector addition states
that if two vectors acting at a point are
represented by the sides of a parallelogram
drawn from that point, their resultant is
represented by the diagonal which passes through
that point of the parallelogram
1.4 Scalars and Vectors

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1.4 Scalars and Vectors
Another method of Adding Vectors
• To add vectors A and B
– place the starting point of B at the ending point of A
– The vector sum or resultant R is the vector joining the
starting point of vector A to the ending point of B
– Conversely, R can also be obtained by placing the
starting point of A at the ending point of B
– Now the resultant is represented by the vector joining
the starting point of B to the ending point of A
• See next slide

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1.4 Scalars and Vectors
A
B
A
B
A
B

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1. Scalar quantities are quantities that only have
magnitudes
2. Vector quantities are quantities that have both
magnitude and direction
3. Parallel vectors can be added arithmetically
4. Non-parallel vectors are added by graphical
means using the parallelogram law

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12. Physical Quantities, Units and Measurement
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1.5 Measurement of Length and Time
Accurate Measurement
• No measurement is perfectly accurate
• Some error is inevitable even with high precision
instruments
• Two main types of errors
– Random errors
– Systematic errors

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1.5 Measurement of Length and Time
Accurate Measurement
• Random errors occur in all measurements.
• Arise when observers estimate the last figure of
an instrument reading
• Also contributed by background noise or
mechanical vibrations in the laboratory.
• Called random errors because they are
unpredictable
• Minimize such errors by averaging a large number
of readings
• Freak results discarded before averaging

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Accurate Measurement
• Systematic errors are not random but constant
• Cause an experimenter to consistently
underestimate or overestimate a reading
• They Due to the equipment being used – e.g. a
ruler with zero error
• may be due to environmental factors – e.g.
weather conditions on a particular day
• Cannot be reduced by averaging, but they can be
eliminated if the sources of the errors are known
1.5 Measurement of Length and Time

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Least count of instruments
The smallest value that can be
measured by the measuring instrument
is called its least count or resolution.

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LC of length measuring instruments
Least count = 1 mm
Ruler scale Vernier Calliper
Least count = 0.1 mm

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Least count = 0.01 mm
Screw Gauge Spherometer
Least count = 0.01 mm
LC of length measuring instruments

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Least count = 1 kg
Weighing scale Electronic balance
Least count = 1 g
LC of length measuring instruments

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Least count = 1 s
Wrist watch Stopwatch
Least count = 0.01 s
LC of length measuring instruments

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Length
• Measuring tape is used to measure relatively long
lengths
• For shorter length, a metre rule or a shorter rule
will be more accurate
1.5 Measurement of Length and Time

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• Correct way to read the scale on a ruler
• Position eye perpendicularly at the mark on the
scale to avoids parallax errors
• Another reason for error: object not align or
arranged parallel to the scale
1.5 Measurement of Length and Time

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• Many instruments do not read exactly zero when
nothing is being measured
• Happen because they are out of adjustment or
some minor fault in the instrument
• Add or subtract the zero error from the reading
shown on the scale to obtain accurate readings
• Vernier calipers or micrometer screw gauge give
more accurate measurements
1.5 Measurement of Length and Time

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