Calculations of angular momentum in dynamics

1. Lab # 4
Angular
Measurement
ML 312
Instrumentation & Measurement Lab

2. 2
Sizes (mm) Increments (mm) No. of Pieces
1.005 0.005 01
1.01-1.09 0.01 09
1.1-1.9 0.1 09
1-9 1 09
10-30 10 03
50 - 01
Total 32
Make a desire dimension of 32.5 mm using M32 gauge block set
Quiz 2

3. 3
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.

4. 4
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

5. 5
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° )

6. 6
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'

7. 7
Angular Measurement
Change 5°25' to decimal degrees
Divide the minutes by 60
Add 0.4167 to 5 = 5.4167°
5°25' = 5.4167°
25 divided by 60 = 0.4167

8. 8
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" = 27.8764°
35 divided by 60 = 0.5833
Added to the 52 minutes, it becomes 52.5833'
52.5833 divided by 60 = .8764
Added to the 27 degrees, it becomes 27.8764°

9. 9
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.
47.75° = 47°45'
75 x 60 = 45
Since there isn't any decimal portion after
the 45, no further work is necessary.

10. 10
Angular Measurement
Change 82.3752° to Degrees, minutes, and
seconds
Multiply the decimal portion by 60
Multiply the decimal minutes by 60
82.3752° = 82°22'30.72"
0.3752 x 60 = 22.512 (the 22 becomes
the minutes) Now add this to the degrees
0.512 x 60 = 30.72 Now add this to the
degrees and minutes to become seconds.
82.3752° = 82°22.512'

11. 11
Angular Measure Tools

12. 12
Angular Measurement
• Most common tools
• Simple Protractor
• Multi-Use Gage
• Combination Set
• Universal bevel protractor
• Sine bar
• Sine plate

13. 13
Protractor

14. 14
Protractor
Whole degree increments

15. 15
Multi-Use Gage
Pre-set positions for
45 and 90 degrees,
59 degree drill point
angle, and whole
degree increments.

16. 16
Multi-Use Gage
Pre-set position for 90 degrees.

17. 17
Multi-Use Gage
Pre-set position for 45 degrees.

18. Combination Set
18
• It is used as a rule, a square, a depth gage, a height gage,
a level and for anglular measurement.

19. USING A COMBINATION SQUARE

20. USING A COMBINATION SQUARE
• Using as a center head
to find the diameter of
a cylinder

22. Using as a protractor head to
determine an angle
• 1. • 3.
• 2. • 4.

23. 23
Combination Set Protractor
Whole degree increments

24. 24
Combination Set
Protractor
Angular
Measure
with
Protract
or Head

25. 25

26. 26
Combination Set
Built-in
Spirit
Level

27. 27
• Precision
angles to within
5' (0.083º)
• Consist of base
• Vernier scale
• Protractor dial
• Sliding blade
• Dial clamp nut
Universal Bevel Protractor

28. 28
Universal Bevel Protractor
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

29. 29
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'

30. Example
30
• The reading is 46° - 20‘

31. 31
Inclinometer

32. 32
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

33. Sine bars
33
• A sine bar is a tool used to measure angles in
metalworking.
• It consists of a hardened, precision ground body with two
precision ground cylinders fixed at each end, the rollers are
positioned at a precise distance and the top of the bar is
parallel to the center line of the rollers.
• The dimension between the two rollers is chosen to be a
whole number (for ease of later calculations)

34. 34
Sine Bar

35. Sine bars
35

36. 36
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.

37. 37
Sine Bars