Math Review
Unit
Lu Jiang
Outline
• Metric System
• Scalar and Vector
• Scienti c Notation
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• Signi cant gures
Why Scientific Notation?
• Physical measurements vary tremendously in magnitude (size).
—Width of Canada
—Thickness of human hair
—Transistor on an integrated circuit
Scientific Notation in Practice
• Which is easier to write and read?
4000,000,000,000
4×1012
• Which is easier to write and read?
0.0000000001m
1×10-9m
Why Do We Need Units?
• What’s the di erence?
135
135cm
• Physics involves the study, prediction, and analysis of real-world events.
• To communicate these events accurately, we must set speci c standards for
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our measurements.
Why Do We Need Units?
• Physics involves the study, prediction, and analysis of real-world events.
• To communicate these events accurately, we must set speci c standards for
our measurements.
• Physicists have agreed to use the Systeme International (SI).
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• The SI system is a subset of the metric system.
Measurement
The comparison
of an unknown
quantity with a
known quantity
Standard
feet
The Systeme International
• Comprised of 7 fundamental units
• Based on powers of 10
• All other units are derived from these 7
—Meter
—Kilogram
—Ampere
—Candela
—Mole
—Kelvin
—Second
How long is one meter?
The distance traveled by light through vacuum in
1/299,792,458 (3.33564095 x 10-9) of a second ——One meter
The meter was originally defined as one ten-millionth (0.0000001 or 10-7)
of the distance passing through Paris from the north pole to the equator.
The distance light travels in one year
——A light-year
<The Three-Body Problem>
• The speed of Trisolaran interstellar fleet reaches the light speed. They are
heading towards earth from 4 light-year away. How long does it take the
fleet to reach earth?
<The Three-Body Problem>
• The speed of Trisolaran interstellar fleet reaches one of ten light speed.
They are heading towards earth from 4 light-year away. How long does it
take the fleet to reach earth?
Earth's circumference
7
10 m
Diameter of single hair
-4
10 m
Diameter of
-7
virus10 m
Scientific Notation
Diameter of an atom
-10
10 m
The Meter
A measure of length, similar to a yard in the English system.
• For measurements smaller than a meter, use
—Centimeter
—Millimeter
—Micrometer
—Nanometer
• For measurements larger than a meter, use
—Kilometer
Kilometer Meter Millimeter Micrometer
•
Base Unit
Converting Fundamental Units
• 5.357km →________m
• 2480m →________km
• 14cm →_________mm
• 182mm →_________m
The Kilogram
Roughly equivalent to 2.2 English pounds.
• For measurements smaller than a kilogram
—Grams
—Milligrams
• For measurements larger than a kilogram
—Megagram (1000kg)
Kilogram Gram
•
Milligram
Base Unit
Converting Fundamental Units
• 5.357kg →________g
• 2480g →________kg
• 156mg →_________g
• 182g →_________kg
Seconds
• The base unit of time is a second.
• Unlike the rest of the metric system, quantities of time are not based on
powers of 10.
• Longer times
—Minute = 60s
—Hour = 60min
— Day = 24hrs
• Shorter times use milliseconds, microseconds, etc.
Multi-Step Conversions
• 2h → _______min
• 1d →_______min
• 1h →_______s
• 10080min →_________day
• 1 year →_______s
Derived Units
Derived units are units made by various combinations of fundamental units.
—Velocity (m/s)
—Acceleration (m/s2)
—Force (kg·m/s2) = (N)
Derived Unit Conversions
• 1km/hr → ________m/s
• 32m/s → ________km/hr