Chapter 1 Introduction, Units, and Dimensional Analysis

Learning Objectives

• Physics and the Laws of Nature• Units of Length, Mass, and Time• Dimensional Analysis• Converting Units• Order-of-Magnitude Calculations• Scalars and Vectors• Problem Solving in Physics

PowerPoint presentations are compiled from Walker 3rd Edition Instructor CD-ROM and Dr. Daniel Bullock’s own resources

Why do we study physics?

• Physics is the study of the fundamental laws of nature.• Aristotle 16th century• Galileo Law of Inertia• Newton 17th century

– Principia– Three laws of motion

• Modern Physics 19th century

Mathematical Nature of Physics

• Newton and Leibniz Calculus• Mathematics is the only language precise enough to

accurately describe the laws of nature. isomorphism • Skills needed for success in this course

– Algebra – Trigonometry – Vector Algebra – Graphical Analysis

Units used in Physics

• Fundamental units– Length (International System, SI meter (m), British foot (ft))– Mass (SI gram (gr), British slug (sl))– Time (SI & British second (s))

• Derived units – combinations of fundamental units– Speed (SI m/s, British ft/s)– Acceleration (SI m/s2, British ft/s2)– Force = mass × acceleration (SI kg·m/s2 = Newton (N),

British pounds (lbs)

Units used in Physics• Length: the meter

– Was: one ten-millionth of the distance from the North Pole to the equator

– Now: the distance traveled by light in a vacuum in 1/299,792,458 of a second

Units used in Physics• Mass: the kilogram

– One kilogram is the mass of a particular platinum-iridium cylinder kept at the International Bureau of Weights and Standards, Sèvres, France.

Units used in Physics• Time: the second

– One second is the time for radiation from a cesium-133 atom to complete 9,192,631,770 oscillation cycles.

Converting units in the SI system• SI system based on powers of ten• Each prefix represents a different

power of ten

KindHector Decked Mr. Deci at the Cinema on Monday

Dimensional Analysis• Any valid physical formula must be dimensionally

consistent – each term must have the same dimensions

From the table:

Distance = velocity × time

Velocity = acceleration × time

Energy = mass × (velocity)2

Converting Units• Converting feet to meters:

1 m = 3.281 ft (this is a conversion factor)

Or: 1 = 1 m / 3.281 ft

316 ft × (1 m / 3.281 ft) = 96.3 m

Note that the units cancel properly – this is the key to using

the conversion factor correctly!• Converting feet2 = meter2

316 ft2 × (1 m / 3.281 ft)2 = 29.35 m2

Scalars and Vectors

• Scalar – a numerical value. May be positive or negative. Examples: temperature, speed, height

• Vector – a quantity with both magnitude and direction. Examples: displacement (e.g., 10 feet north), force, magnetic field

Problem Solving in Physics

1. Read the problem carefully2. Sketch the system3. Visualize the physical process4. Strategize5. Identify appropriate equations6. Solve the equations7. Check your answer8. Explore limits and special cases

Chapter 1 Summary

• Physics is based on a small number of laws and principles

• Units of length are meters; of mass, kilograms; and of time, seconds

• All terms in an equation must have the same dimensions

• Convert one unit to another by multiplying by their ratio

• Scalars are numbers; vectors have both magnitude and direction

• Problem solving: read, sketch, visualize, strategize, identify equations, solve, check, explore limits