0. Physical quantities
and
SI units
Subtopics
1.
2.
3.
4.
Physical quantities
SI units
Errors and uncertainties
Scalars and vectors
0.1 Physical quantities
Our goals:
1.
2.
Understand that all physical quantities consist of a numerical magnitude and a unit
make reasonable estimate of physical quantities included within the syllabus
0.1 Physical quantity
definition: a feature of something which can be measured, for example, length, weight, or
time. Consist of a magnitude and a unit.
Example of physical quantity:
magnitude
unit
0.1 Physical quantities
questions:
1.
2.
estimate the mass of an apple
estimate the volume of a basketball
0.2 SI units
Our goals:
1.
2.
3.
4.
recall the following SI base quantities and their units: mass (kg), length (m), time (s), current
(A), temperature (K)
express derived units as products or quotients of the SI base units and use the derived units for
quantities listed in this syllabus as appropriate
use SI base units to check the homogeneity of physical equations
recall and use the following prefixes and their symbols to indicate decimal submultiples or
multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci
(d), kilo (k), mega (M), giga (G), tera (T)
0.2 SI units
Base units
Derive units
definiton : seven fundamental SI
definition : product of base units
example of some derive units
0.2 SI units
Determine derive units:
1.
2.
write down the formula of a quantity
write each base unit from the formula
example:
determine the base units of speed?
0.2 SI units
Determine the units of the following quantities:
1.
Density
2.
Pressure
0.2 SI units
Homogenity of units means each term has the same base units.
example :
unit of u and at have the same unit as v.
question:
show that the left hand side of the equation : pressure + ½ x density x speed^2 = constant
is homogeneous and find the base units of the constant on the right hand side
0.2 SI units
Prefixes
0.3 Errors and uncertainties
Our goals:
1.
2.
3.
understand and explain the effects of systematic errors (including zero errors) and random
errors in measurements
understand the distinction between precision and accuracy
assess the uncertainty in a derived quantity by simple addition of absolute or percentage
uncertainties
0.3 Error and uncertainties
Systematic error : all readings being either above or
below the accepted value and cannot eliminated by
repeating reading and then averaging.
Examples of systematic errors:
1.
zero error on an instrument
2.
3.
wrongly caliberated scale
reaction time of experimenter
Random error : readings being scattered around the
accepted value, may be reduced by repeating a reading
and averaging, and by plotting a graph and drawing a
best-fit line. examples:
1.
2.
reading a scale from different angles
Accuracy and precision
Uncertainties:
1.
Absolute uncertainty
:
absolute uncertainty
2.
percentage uncertainty
:
Combining uncertainties:
1.
If formula is addition or substraction, absolute uncertainty of each quantity added, example:
2.
If formula is multiplication or divisor, percentage uncertainty of each quantity added, example:
Percentage uncertainty of P
Absolute uncertainty of P
3.
If formula is power/root, percentage uncertainty multiply by factor of power of the quantity, example:
Define absolute uncertainty of
with:
0.4 Scalars and vectors
Our goals:
1.
2.
3.
understand the difference between scalar and vector quantities and give examples of scalar
and vector quantities included in the syllabus
add and subtract coplanar vectors
represent a vector as two perpendicular components
0.4 Scalars and vectors
Scalar : a quantity which can be describe fully by giving its magnitude.
Vector: a quantity which has magnitude and direction
0.4 Scalars and vectors
Vector Representation
0.4 Scalars and vectors
Addition of vector : connects vectors
0.4 Scalar and vectors
Resolution of vectors