Website Notes for Ch. 1 - The Mathematics of Physics.

1. The scientific method is probably the most efficient problem-solving

tool ever devised. There are 6 steps in the scientific method: (I) Define

the problem, (II) Gather information, (III) State your hypothesis, (IV) Test

the hypothesis, (V) Form your conclusion, (VI) Publish the results. The

scientific method is the process by which scientists, collectively and over

time, endeavor to construct an accurate (that is, reliable, consistent and

non-arbitrary) representation of the natural world.

2. The Metric System (Systeme International, SI) was first introduced by

the French Academy of Science in 1795 as an attempt to unify existing

systems. The SI contains the basic units for length (meter, m), mass

(kilogram, kg), and time (second, s), with speed (m/s), volume (m³),

and density (kg/m³) as some derived units.

3. All calculations must be done observing significant digits and scientific

notation. When a number is expressed in scientific notation, the number

of significant figures is the number of digits needed to express the number

to within the uncertainty of measurement.  We always round to the least

precise measurement. Here is an example problem, if you have to

multiply 2.5 cm x 1.23 cm the result is 3.1 cm² .

4. The number of significant figures of a product or quotient of two or

more quantities is equal to the smallest number of significant figures for

the quantities involved. For example, if you multiply 5.2 x 3.751 x 6.43,

your answer must be written using only two significant digits as 130.

For addition or subtraction, the number of significant figures is determined

with the smallest significant figure of all the quantities involved. For

example, the sum 10.234 + 5.2 + 100.3234 is 115.7574, but should be

written 115.8 (with rounding), since the quantity 5.2 is significant only

to 0.1.

5. Order of magnitude (power of 10) calculations provide quick estimates

for answers to certain questions. An order of magnitude calculation is an

estimate to determine if a more precise calculation is necessary. We round

off or guess at various inputs to obtain a result that is usually reliable to

within a factor of 10. Specifically, to get the order of magnitude of a given

quantity, we round off to the closest power of 10 (example: 75 kg is

expressed as 10² kg). Another example, the average distance from the

Earth to the Sun is 93,000,000 miles. In scientific notation this is

9.3x10⁷ miles. But since 9.3 is closest to 10¹, we would express the order

of magnitude as 10⁸ miles.

6. A frame of reference is a coordinate system for specifying the precise

7. Accuracy refers to the agreement of a measured value with an accepted

 value. Percent error measures accuracy.

8. There are occasions when an error in measurement is due to parallax

which is the apparent shift in position of an object when it is viewed from

different angles.

9. Precision is the agreement of a set of measured values with each other,

and is determined by the fineness of divisions on a scale. It can be

measured by average deviation.

10. All graphs are plotted with the independent (control) variable on the

x-axis, and the dependent (measured) variable on the y-axis.

11. Graphs can show direct (linear), inverse (hyperbolic), periodic

(sinusoidal), quadratic (parabolic), or chaotic relationships.

12. All equations must be dimensionally correct. We use dimensional

analysis (factor labeling) to determine if equations are correct.

13. The density of a substance is defined as its mass per unit volume. We

use the Greek letter rho, ρ, for density and the equation is ρ = m / V.

14. Some equations that you may remember from Mathematics are

A = πr², C = 2πr, V = Lwh, V = πr²h, V = 4/3 πr³, and d = vt. Notice that

variables in Physics are case sensitive. For example, A is area, but a

is acceleration. Another example, T is temperature, but t is time.

15. We also need to remember SOHCAHTOA to compute the value of

unknown sides and angles of right triangles.

16. We need these steps to solve any problem in Physics:

And Always Remember...  "From  Newtonian Mechanics,   Through Quantum Theory,   Without  Physics,   Life Would Be Dreary."

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