PHYSICAL QUANTITIES

General Physics I

Physical quantities

• are classified as fundamental or basic and derived quantities.

• can be expressed as combinations of only four fundamental physical quantities: length, mass, time, and electric current.

• have a numerical value and a unit of measurement which are standardized.

  We define physical quantity either in two ways: specifying how it is measured or stating how it is calculated from other measurements. 

Standard and Non-Standard Units of Measurements

1. The English and Metric System

Fundamental Quantities: The standard units for time (second), length (meter), mass (kilogram), electric current (ampere), thermodynamic temperature (Kelvin), amount of substance (mole), and luminous intensity (candle).

What are some examples of units in the English System?

For length in the English system is in inches while for time is still in seconds. 

DERIVED QUANTITIES! Derived quantities are quantities with two or more fundamental quantities involved.

What are some examples of derived quantities?

1. One Newton = 1 kg-m/s squared which has 3 fundamental quantities

2. One Joule = 1 kg-m squared/ squared which has 3 fundamental quantities 

3. Speed =  m’s which has 2 fundamental quantities

4. Volume = m cube which has 1 fundamental quantity three times

If quantities are in the English system, they have to be converted into the metric system of measurement.

B. Nonstandard Units of Measurement  What are some nonstandard measures?

1. Foot -> length of your foot

2. Palm -> width of four fingers

3. Span -> from tip of little finger to tip of thumb

4. Arm -> length from shoulder to the tip of the middle 

5. Thumb -> distance from the tip to the base around 2 inches

6. Cublt -> distance from the tip of an elbow to the tip of the middle finger

7. Hand -> width along the knuckles from the left side of your thumb to the right side of your little finger with all five fingers side by side

Conversion of Units in the English and Metric System

Some Useful Conversions

10 mm = 1 cm

1 in = 2.54 cm

100 cm = 1 m

1000g = 1 kg

1000m = 1km

1 lb = 0.45 kg

12 inches = 1 feet

60 second = 1 minute

3 feet = 1 yard

60 minutes = 1 hour

1 mile = 1.009km

24 hours = 1 day

Writing In Scientific Notation 

The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of 10 in the metric system represents a different order of magnitude.

All quantities that can be expressed on a specific power are said to be of the same order of magnitude.

A number is written in scientific notation if it is expressed in the form a < 10 n top, where a is areal number less than 10 and n is an integer. Note as the value of n increases, the number value decreases.

The numbers 800 and 450 are of the same order of magnitude since both can be written as a power of 10.

800 = 8.00 < 10 squared and that 450 = 4.50 x 10 squared

 SIGNIFICANT DIGITS

In many cases the uncertainty of a number is not stated explicitly Instead the uncertainty is indicated by the number of moaningful digits, or significant digits, in tho measured value.

EXAMPLE 1,10, IDENTIFYING SIGNIFICANT FIGURES

0. 00005 

15450.0

87.990

30.42

25000

120035.789

100.000

EXAMPLE 1.18. IDENTIFYING SIGNIFICANT FIGURES

1.0,0009 → has only 1 significant digit Tho soroes in this

decimal are placeholders that indicate the decimal point

15450.0 -> has 6 significant digits. The zeroes indicate that a measurement was made to the 0.1 point decimal point, so the zeroes are significant 

87.990 → has 5 significant figures, The Rnal zoro Indicates that a monument was made to tho 0,001 decimal point

30.42 → has 4 significant figures. Any zeroes located in between significant figures in between significant figures in a number are significant

25000 → has 2 significant only digits. The three zeroes to the right are not significant sínce they are place values.

120036,780 = has 9 significant digits.  All 9 digits are significant over the two zeroes in the middle.

100.000 - has 6 significant digits.

PRECISION

The precision of a measurement system refers to how close the agreement is between repeated measurements (which are repeated under the same conditions)

 When measurements are done, precision is the amount of consistency of independent measurements and the reliability of reproducibility of the measurements.

The precision of the measurements refers to the spread of the measured values. One way to analyze is to look at the range of values.

Using the information shown in the previous example the measured values deviated from each other by at most 0.3 in.

The measurements were relatively precise because they did not vary too much in value.

The measurements in the proper example are both accurate and precise.

ACCURATE BUT NOT PRECISE AND VICE VERSA

• Can measurements be accurate but not precise?

• Can measurements be precise but not accurate?

• Can measurements be both not precise and not accurate?

SYSTEMATIC ERRORS

 are caused by faulty Instrument or incorrect handling of there Instruments. Tend to be consistent in magnitude and/or reaction. if the magnitude and direction of the error is known, accuracy can be improved by additive and proportional corrections.

RANDOM ERRORS

ccur whoa thero aro variations in tha

environment or via the measurement techniques

Vary in magnitude and direction. It is possible to calculate the average of a set of measure positions, however, and that average is unlikely to be  more accurate than most of the menouramento. Random errors use statistical analysis. Averaging the large number of observations can reduce errors.

CAUSES OF ERROR IN LABORATORY EXPERIMENTS

1. Inadequate Definition (either systematic or random)

2. Unable to Include a factor (systematic)

3. Factors due to the environment (either systematic or random)

4. Listed scale of the Instrument (random)

5. Limited scale of the Instrument (random)

6. Unable to calibrate or check zero scale of thor lnstrument (systematic)

7. Variations In the physical instrument (random)

8. Parallarax (other systematic or random)

9. Personal Errors

The Concept of Uncertainty

Uncertainty is a quantitative measure of how much your measured values deviate from the espected value.

SOME FACTORS CONTRIBUTING TO UNCERTAINTY

• Limitations of the measuring defice

• The skill of the person making the measurement

• Irregularities in the object being measured

• Percentage errors express an uncertainty or discrepancy in a value as a percentage of the value. An uncertainty describes the range of values a result of measurement can take, and is related to reliability or precision.