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Angular Measurement. Session 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.

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AngularMeasurement

Session 2


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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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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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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 = 87.25 Degrees ( 87.25° )


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Angular Measurement

  • Minutes and seconds can each be expressed as decimal or fractional degrees.

  • 1 Minute ( 1' ) = 1/60th of a Degree = 0.01667°

  • 1 Second ( 1" ) = 1/60th of a Minute = 0.01667'


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Angular Measurement

Change 5°25' to decimal degrees

Divide the minutes by 60

25 divided by 60 = 0.4167

Add 0.4167 to 5 = 5.4167°

5°25' = 5.4167°


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Angular Measurement

Change 27°52'35" to decimal degrees

Divide the seconds by 60, add to minutes

35 divided by 60 = 0.5833

Added to the 52 minutes, it becomes 52.5833'

Divide the minutes by 60, add to degrees

52.5833 divided by 60 = .8764

Added to the 27 degrees, it becomes 27.8764°

27°52'35" = 27.8764°


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Angular Measurement

Change 47.75° to degrees, minutes, and seconds

Multiply the decimal portion by 60

75 x 60 = 45

This decimal .75 becomes 45 minutes. Add this to the degrees.

Since there isn't any decimal portion after the 45, no further work is necessary.

47.75° = 47°45'


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Angular Measurement

Change 82.3752° to Degrees, minutes, and seconds

Multiply the decimal portion by 60

0.3752 x 60 = 22.512 (the 22 becomes the minutes) Now add this to the degrees

82.3752° = 82°22.512'

Multiply the decimal minutes by 60

0.512 x 60 = 30.72 Now add this to the degrees and minutes to become seconds.

82.3752° = 82°22'30.72"



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Angular Measurement

  • Most common tools

    • Simple Protractor

    • Multi-Use Gage

    • Combination Set

    • Universal bevel protractor

    • Sine bar

    • Sine plate



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Protractor

Whole degree increments


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Multi-Use Gage

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


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Multi-Use Gage

Pre-set position for 90 degrees.


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Multi-Use Gage

Pre-set position for 45 degrees.


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Multi-Use Gage

Measuring 59 degree drill point angle.


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Combination Set Protractor

Whole degree increments


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Protractor Head

Whole degree increments


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Protractor

Built-in Spirit Level


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Protractor

Angular Measure with Protractor Head



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Universal Bevel Protractor

  • Precision angles to within 5' (0.083º)

  • Consist of base

    • Vernier scale

    • Protractor dial

    • Sliding blade

    • Dial clamp nut


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Vernier Protractor

  • Used to measure obtuse angle (90º-180º)

  • Acute-angle attachment fastened to protractor to measure angles less than 90º

  • Main scale divided intotwo arcs of 180º

    • Scale divided into 12 spaces on each side of 0

    • If zero on vernier scalecoincides with line on main: reading in degrees


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Fourth

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

  • Multiply number by 5' and add to degrees on protractor dial

50º

4 x 5'= 20'

Reading =

50º 20'



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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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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 .00005 in. in 5 inches or 0.001 mm in 100 mm.




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