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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

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.

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

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° )

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'

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°

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°

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'

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"

Angular Measurement

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

Protractor

Whole degree increments

Multi-Use Gage

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

Multi-Use Gage

Pre-set position for 90 degrees.

Multi-Use Gage

Pre-set position for 45 degrees.

Multi-Use Gage

Measuring 59 degree drill point angle.

Combination Set Protractor

Whole degree increments

Protractor Head

Whole degree increments

Protractor

Built-in Spirit Level

Protractor

Angular Measure with Protractor Head

Universal Bevel Protractor

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

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

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'

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

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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