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1 Angular Measurement Session 2

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2 Angular Measurement Circles are divided into 360 equal parts, each being a degree. Each of these degrees can be evenly divided into 60 equal parts. These parts are called minutes. These minutes can be evenly divided into 60 equal parts. These parts are called minutes.

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3 Angular Measurement 1 Circle = 360 Degrees ( 360° ) 1 Degree ( 1° ) = 1/360th of a Circle 1 Degree ( 1°) = 60 Minutes ( 60' ) 1 Minute ( 1' ) = 1/60th of a Degree 1 Minute ( 1') = 60 Seconds ( 60" ) 1 Second ( 1" ) = 1/60th of a Minute

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4 Angular Measurement The unit of degree can also be divided into either decimal or fractional parts and is referred to as decimal degrees or fractional degrees respectively. 1½ Degree = 1.5 Degree ( 1.5°) 87¼ Degrees = Degrees ( 87.25° )

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5 Angular Measurement Minutes and seconds can each be expressed as decimal or fractional degrees. 1 Minute ( 1' ) = 1/60th of a Degree = ° 1 Second ( 1" ) = 1/60th of a Minute = '

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6 Angular Measurement Change 5°25' to decimal degrees Divide the minutes by 60 Add to 5 = ° 5°25' = ° 25 divided by 60 =

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7 Angular Measurement Change 27°52'35" to decimal degrees Divide the seconds by 60, add to minutes Divide the minutes by 60, add to degrees 27°52'35" = ° 35 divided by 60 = Added to the 52 minutes, it becomes ' divided by 60 =.8764 Added to the 27 degrees, it becomes °

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8 Angular Measurement Change 47.75° to degrees, minutes, and seconds Multiply the decimal portion by 60 This decimal.75 becomes 45 minutes. Add this to the degrees ° = 47°45' 75 x 60 = 45 Since there isn't any decimal portion after the 45, no further work is necessary.

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9 Angular Measurement Change ° to Degrees, minutes, and seconds Multiply the decimal portion by 60 Multiply the decimal minutes by ° = 82°22'30.72" x 60 = (the 22 becomes the minutes) Now add this to the degrees x 60 = Now add this to the degrees and minutes to become seconds ° = 82°22.512'

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10 Angular Measure Tools

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11 Angular Measurement Most common tools Simple Protractor Multi-Use Gage Combination Set Universal bevel protractor Sine bar Sine plate

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12 Protractor

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13 Protractor Whole degree increments

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14 Multi-Use Gage Pre-set positions for 45 and 90 degrees, 59 degree drill point angle, and whole degree increments.

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15 Multi-Use Gage Pre-set position for 90 degrees.

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16 Multi-Use Gage Pre-set position for 45 degrees.

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17 Multi-Use Gage Measuring 59 degree drill point angle.

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19 Combination Set Protractor Whole degree increments

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20 Protractor Head Whole degree increments

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21 Protractor Built-in Spirit Level

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22 Protractor Angular Measure with Protract or Head

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23 Transfer-type Protractors

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24 Precision angles to within 5' (0.083º) Consist of base Vernier scale Protractor dial Sliding blade Dial clamp nut Universal Bevel Protractor

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25 Vernier Protractor Used to measure obtuse angle (90º-180º) Acute-angle attachment fastened to protractor to measure angles less than 90º Main scale divided into two arcs of 180º Scale divided into 12 spaces on each side of 0 If zero on vernier scale coincides with line on main: reading in degrees

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26 Reading a Vernier Protractor Note number of whole degrees between zero on main scale and zero on vernier scale Proceeding in same direction, note which vernier line coincides with main scale line 50º Fourth Multiply number by 5' and add to degrees on protractor dial 4 x 5'= 20' Reading = 50º 20'

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27 Inclinometer

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28 Sine Bars Used when accuracy of angle must be checked to less than 5 minutes Consists of steel bar with two cylinders of equal diameter fastened near ends Centers of cylinders exactly 90º to edge Distance between centers usually 5 or 10 inches and 100 or 200 millimeters. Made of stabilized tool hardened steel

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29 Sine Bar

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30 Sine Bars Used on surface plates and any angle by raising one end of bar with gage blocks Made 5 inch or in multiples of 5 or 100 millimeters or multiple of 100 Distance between lapped cylinders. Face accurate to within in. in 5 inches or mm in 100 mm.

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31 Sine Bars

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32 Sine Plate

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