Dimensions of Physics

The essence of physics is to measure the observable world and describe the principles that underlie everything in creation. This usually involves mathematical formulas.

The Metric System first established in France and followed voluntarily in other countries renamed in 1960 as the SI (Système International d’Unités) seven fundamental units

Dimension can refer to the number of spatial coordinates required to describe an object can refer to a kind of measurable physical quantity

Dimension the universe consists of three fundamental dimensions: space time matter

Length the meter is the metric unit of length definition of a meter: the distance light travels in a vacuum in exactly 1/299,792,458 second.

Time defined as a nonphysical continuum that orders the sequence of events and phenomena SI unit is the second

Mass a measure of the tendency of matter to resist a change in motion mass has gravitational attraction

The Seven Fundamental SI Units length time mass thermodynamic temperature meter second kilogram kelvin

The Seven Fundamental SI Units amount of substance electric current luminous intensity mole ampere candela

SI Derived Units involve combinations of SI units examples include: area and volume force (N = kg m/s²) work (J = N m)

Conversion Factors any factor equal to 1 that consists of a ratio of two units You can find many conversion factors in Appendix C of your textbook.

Unit Analysis First, write the value that you already know. 18m

Unit Analysis Next, multiply by the conversion factor, which should be written as a fraction. Note that the old unit goes in the denominator. 18× 100 cm 1 m m

Unit Analysis Then cancel your units. Remember that this method is called unit analysis. 18× 100 cm 1 m m

Unit Analysis Finally, calculate the answer by multiplying and dividing. =1800 cm18× 100 cm 1 m m

Unit Analysis Bridge

Convert m to km m × 1 km 1000 m = 13.4 km Sample Problem #1

How many seconds are in a week? 1 wk × 7 d 1 wk =604,800 s × 24 h 1 d × 60 min 1 h × 60 s 1 min Sample Problem #2

Convert 35 km to mi, if 1.6 km ≈ 1 mi. 35 km × 1 mi 1.6 km ≈ 21.9 mi Sample Problem #3

Principles of Measurement

Instruments tools used to measure critical to modern scientific research man-made

comparing the object being measured to the graduated scale of an instrument Accuracy

dependent upon: quality of original design and construction how well it is maintained reflects the skill of its operator Accuracy

the simple difference of the observed and accepted values may be positive or negative Error

absolute error—the absolute value of the difference Error

Percent Error observed – accepted accepted × 100%

a qualitative evaluation of how exactly a measurement can be made describes the exactness of a number or measured data Precision

some quantities can be known exactly definitions countable quantities Precision

irrational numbers can be specified to any degree of exactness desired potentially unlimited precision Precision

When you use a mechanical metric instrument (one with scale subdivisions based on tenths), measurements should be estimated to the nearest 1/10 of the smallest decimal increment.

The last digit that has any significance in a measurement is estimated.

Truth in Measurements and Calculations

Remember: The last (right- most) significant digit is the estimated digit when recording measured data. Significant Digits

Rule 1: SD’s apply only to measured data. Significant Digits

Rule 2: All nonzero digits in measured data are significant. Significant Digits

Rule 3: All zeros between nonzero digits in measured data are significant. Significant Digits

Rule 4: For measured data containing a decimal point: Significant Digits All zeros to the right of the last nonzero digit (trailing zeros) are significant

Rule 4: For measured data containing a decimal point: Significant Digits All zeros to the left of the first nonzero digit (leading zeros) are not significant

Rule 5: For measured data lacking a decimal point: Significant Digits No trailing zeros are significant

Scientific notation shows only significant digits in the decimal part of the expression. Significant Digits

A decimal point following the last zero indicates that the zero in the ones place is significant. Significant Digits

...and be careful when using your calculator!

Rule 1: All units must be the same before you can add or subtract. Adding and Subtracting

Rule 2: The precision cannot be greater than that of the least precise data given. Adding and Subtracting

Rule 1: A product or quotient of measured data cannot have more SDs than the measurement with the fewest SDs. Multiplying and Dividing

Rule 2: The product or quotient of measured data and a pure number should not have more or less precision than the original measurement. Multiplying and Dividing

Rule 1: If the operations are all of the same kind, complete them before rounding to the correct significant digits. Compound Calculations

Rule 2: If the solution to a problem requires a combination of both addition/subtraction and multiplication/division... Compound Calculations

(1) For intermediate calculations, underline the estimated digit in the result and retain at least one extra digit beyond the estimated digit. Drop any remaining digits. Compound Calculations

(2) Round the final calculation to the correct significant digits according to the applicable math rules, taking into account the underlined estimated digits in the intermediate answers. Compound Calculations

What about angles and trigonometry?

The SI uses radians. A radian is the plane angle that subtends a circular arc equal in length to the radius of the circle. Angles in the SI

2π radians = 360° Angles in the SI Angles measured with a protractor should be reported to the nearest 0.1 degree.

Degrees to Radians: Conversions Multiply the number of degrees by π/180.

Radians to Degrees: Conversions Multiply the number of radians by 180/π.

Report angles resulting from trigonometric calculations to the lowest precision of any angles given in the problem. Angles in the SI

Assume that trigonometric ratios for angles given are pure numbers; SD restrictions do not apply. Angles in the SI

Problem Solving

Read the exercise carefully! What information is given? What information is sought? Make a basic sketch

Problem Solving Determine the method of solution Substitute and solve Check your answer for reasonableness

Reasonable Answers Does it have the expected order of magnitude? Make a mental estimate Be sure to simplify units Express results to the correct number of SDs