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Dimensions of Physics

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

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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

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

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

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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.

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

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

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

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

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

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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.

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

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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

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

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

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Unit Analysis Bridge

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Convert 13400 m to km. 13400 m × 1 km 1000 m = 13.4 km Sample Problem #1

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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

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

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Principles of Measurement

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

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

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

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

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absolute error—the absolute value of the difference Error

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Percent Error observed – accepted accepted × 100%

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

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some quantities can be known exactly definitions countable quantities Precision

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

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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.

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

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Truth in Measurements and Calculations

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

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

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

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

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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

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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

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

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

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

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...and be careful when using your calculator!

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

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

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

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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

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

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

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(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

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(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

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What about angles and trigonometry?

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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

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

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

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

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

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

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Problem Solving

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

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

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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

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