Home » Archimedes archive » Acorn User » AU 1997-01 B.adf » Regulars » StarInfo/Allen/!Ignotum/Formulae/Formulae/Mech
StarInfo/Allen/!Ignotum/Formulae/Formulae/Mech
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn User » AU 1997-01 B.adf » Regulars |
| Filename: | StarInfo/Allen/!Ignotum/Formulae/Formulae/Mech |
| Read OK: | ✔ |
| File size: | 068B bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Mechanics # New entries should take the form of: # Formula # Note 1 # Note 2 # Note 3 # Note 4 # Note 5 # Formula # Note 1 # And so on... # To fit snugly into the window, each line should be no longer # than 42 characters. # There is a limit of 25 formulas per topic. # Any notes should be made here, at the beginning and should # be preceeded by a hash (#). a.b=|a||b|cosx The dot/scalar product: a and b are two vectors x is the angle between them e=v2/v1 For two colliding objects: e=coefficient of restitution v2=speed of separation v1=speed of approach C=rsinx/x For a circular arc of angle 2x: C=distance of centre of mass from centre r=radius C=2rsinx/3x For a circular sector of angle 2x: C=distance of centre of mass from centre r=radius C=3h/4 For a solid cone: C=distance of centre of mass from vertex h=height of cone C=2h/3 For a conical shell: C=distance of centre of mass from vertex h=height of cone C=3r/8 For a solid hemisphere: C=distance of centre of mass from plane face r=radius C=r/2 For a hemispherical shell: C=distance of centre of mass from plane face r=radius MI=ml�/3 For a uniform rod, length 2l: MI=moment of inertia about axis through centre, perpendicular to length m=mass MI=mr� For a uniform hoop, radius r: MI=moment of inertia about axis through centre perpendicular to plane m=mass MI=mr�/2 For a uniform disc, radius r: MI=moment of inertia about axis through centre perpendicular to plane m=mass MI=2mr�/5 For a uniform solid sphere, radius r: MI=moment of inertia about the diameter m=mass
00000000 23 20 4d 61 74 68 73 20 3e 20 4d 65 63 68 61 6e |# Maths > Mechan| 00000010 69 63 73 0a 0a 23 20 4e 65 77 20 65 6e 74 72 69 |ics..# New entri| 00000020 65 73 20 73 68 6f 75 6c 64 20 74 61 6b 65 20 74 |es should take t| 00000030 68 65 20 66 6f 72 6d 20 6f 66 3a 0a 23 20 20 20 |he form of:.# | 00000040 20 20 46 6f 72 6d 75 6c 61 0a 23 20 20 20 20 20 | Formula.# | 00000050 4e 6f 74 65 20 31 0a 23 20 20 20 20 20 4e 6f 74 |Note 1.# Not| 00000060 65 20 32 0a 23 20 20 20 20 20 4e 6f 74 65 20 33 |e 2.# Note 3| 00000070 0a 23 20 20 20 20 20 4e 6f 74 65 20 34 0a 23 20 |.# Note 4.# | 00000080 20 20 20 20 4e 6f 74 65 20 35 0a 23 20 20 20 20 | Note 5.# | 00000090 20 46 6f 72 6d 75 6c 61 0a 23 20 20 20 20 20 4e | Formula.# N| 000000a0 6f 74 65 20 31 0a 23 20 20 20 20 20 41 6e 64 20 |ote 1.# And | 000000b0 73 6f 20 6f 6e 2e 2e 2e 0a 23 20 54 6f 20 66 69 |so on....# To fi| 000000c0 74 20 73 6e 75 67 6c 79 20 69 6e 74 6f 20 74 68 |t snugly into th| 000000d0 65 20 77 69 6e 64 6f 77 2c 20 65 61 63 68 20 6c |e window, each l| 000000e0 69 6e 65 20 73 68 6f 75 6c 64 20 62 65 20 6e 6f |ine should be no| 000000f0 20 6c 6f 6e 67 65 72 0a 23 20 74 68 61 6e 20 34 | longer.# than 4| 00000100 32 20 63 68 61 72 61 63 74 65 72 73 2e 0a 23 20 |2 characters..# | 00000110 54 68 65 72 65 20 69 73 20 61 20 6c 69 6d 69 74 |There is a limit| 00000120 20 6f 66 20 32 35 20 66 6f 72 6d 75 6c 61 73 20 | of 25 formulas | 00000130 70 65 72 20 74 6f 70 69 63 2e 0a 0a 23 20 41 6e |per topic...# An| 00000140 79 20 6e 6f 74 65 73 20 73 68 6f 75 6c 64 20 62 |y notes should b| 00000150 65 20 6d 61 64 65 20 68 65 72 65 2c 20 61 74 20 |e made here, at | 00000160 74 68 65 20 62 65 67 69 6e 6e 69 6e 67 20 61 6e |the beginning an| 00000170 64 20 73 68 6f 75 6c 64 0a 23 20 62 65 20 70 72 |d should.# be pr| 00000180 65 63 65 65 64 65 64 20 62 79 20 61 20 68 61 73 |eceeded by a has| 00000190 68 20 28 23 29 2e 0a 0a 61 2e 62 3d 7c 61 7c 7c |h (#)...a.b=|a||| 000001a0 62 7c 63 6f 73 78 0a 54 68 65 20 64 6f 74 2f 73 |b|cosx.The dot/s| 000001b0 63 61 6c 61 72 20 70 72 6f 64 75 63 74 3a 0a 61 |calar product:.a| 000001c0 20 61 6e 64 20 62 20 61 72 65 20 74 77 6f 20 76 | and b are two v| 000001d0 65 63 74 6f 72 73 0a 78 20 69 73 20 74 68 65 20 |ectors.x is the | 000001e0 61 6e 67 6c 65 20 62 65 74 77 65 65 6e 20 74 68 |angle between th| 000001f0 65 6d 0a 0a 0a 65 3d 76 32 2f 76 31 0a 46 6f 72 |em...e=v2/v1.For| 00000200 20 74 77 6f 20 63 6f 6c 6c 69 64 69 6e 67 20 6f | two colliding o| 00000210 62 6a 65 63 74 73 3a 0a 65 3d 63 6f 65 66 66 69 |bjects:.e=coeffi| 00000220 63 69 65 6e 74 20 6f 66 20 72 65 73 74 69 74 75 |cient of restitu| 00000230 74 69 6f 6e 0a 76 32 3d 73 70 65 65 64 20 6f 66 |tion.v2=speed of| 00000240 20 73 65 70 61 72 61 74 69 6f 6e 0a 76 31 3d 73 | separation.v1=s| 00000250 70 65 65 64 20 6f 66 20 61 70 70 72 6f 61 63 68 |peed of approach| 00000260 0a 0a 43 3d 72 73 69 6e 78 2f 78 0a 46 6f 72 20 |..C=rsinx/x.For | 00000270 61 20 63 69 72 63 75 6c 61 72 20 61 72 63 20 6f |a circular arc o| 00000280 66 20 61 6e 67 6c 65 20 32 78 3a 0a 43 3d 64 69 |f angle 2x:.C=di| 00000290 73 74 61 6e 63 65 20 6f 66 20 63 65 6e 74 72 65 |stance of centre| 000002a0 20 6f 66 20 6d 61 73 73 20 66 72 6f 6d 20 63 65 | of mass from ce| 000002b0 6e 74 72 65 0a 72 3d 72 61 64 69 75 73 0a 0a 0a |ntre.r=radius...| 000002c0 43 3d 32 72 73 69 6e 78 2f 33 78 0a 46 6f 72 20 |C=2rsinx/3x.For | 000002d0 61 20 63 69 72 63 75 6c 61 72 20 73 65 63 74 6f |a circular secto| 000002e0 72 20 6f 66 20 61 6e 67 6c 65 20 32 78 3a 0a 43 |r of angle 2x:.C| 000002f0 3d 64 69 73 74 61 6e 63 65 20 6f 66 20 63 65 6e |=distance of cen| 00000300 74 72 65 20 6f 66 20 6d 61 73 73 20 66 72 6f 6d |tre of mass from| 00000310 20 63 65 6e 74 72 65 0a 72 3d 72 61 64 69 75 73 | centre.r=radius| 00000320 0a 0a 0a 43 3d 33 68 2f 34 0a 46 6f 72 20 61 20 |...C=3h/4.For a | 00000330 73 6f 6c 69 64 20 63 6f 6e 65 3a 0a 43 3d 64 69 |solid cone:.C=di| 00000340 73 74 61 6e 63 65 20 6f 66 20 63 65 6e 74 72 65 |stance of centre| 00000350 20 6f 66 20 6d 61 73 73 20 66 72 6f 6d 20 76 65 | of mass from ve| 00000360 72 74 65 78 0a 68 3d 68 65 69 67 68 74 20 6f 66 |rtex.h=height of| 00000370 20 63 6f 6e 65 0a 0a 0a 43 3d 32 68 2f 33 0a 46 | cone...C=2h/3.F| 00000380 6f 72 20 61 20 63 6f 6e 69 63 61 6c 20 73 68 65 |or a conical she| 00000390 6c 6c 3a 0a 43 3d 64 69 73 74 61 6e 63 65 20 6f |ll:.C=distance o| 000003a0 66 20 63 65 6e 74 72 65 20 6f 66 20 6d 61 73 73 |f centre of mass| 000003b0 20 66 72 6f 6d 20 76 65 72 74 65 78 0a 68 3d 68 | from vertex.h=h| 000003c0 65 69 67 68 74 20 6f 66 20 63 6f 6e 65 0a 0a 0a |eight of cone...| 000003d0 43 3d 33 72 2f 38 0a 46 6f 72 20 61 20 73 6f 6c |C=3r/8.For a sol| 000003e0 69 64 20 68 65 6d 69 73 70 68 65 72 65 3a 0a 43 |id hemisphere:.C| 000003f0 3d 64 69 73 74 61 6e 63 65 20 6f 66 20 63 65 6e |=distance of cen| 00000400 74 72 65 20 6f 66 20 6d 61 73 73 20 66 72 6f 6d |tre of mass from| 00000410 20 70 6c 61 6e 65 0a 66 61 63 65 0a 72 3d 72 61 | plane.face.r=ra| 00000420 64 69 75 73 0a 0a 43 3d 72 2f 32 0a 46 6f 72 20 |dius..C=r/2.For | 00000430 61 20 68 65 6d 69 73 70 68 65 72 69 63 61 6c 20 |a hemispherical | 00000440 73 68 65 6c 6c 3a 0a 43 3d 64 69 73 74 61 6e 63 |shell:.C=distanc| 00000450 65 20 6f 66 20 63 65 6e 74 72 65 20 6f 66 20 6d |e of centre of m| 00000460 61 73 73 20 66 72 6f 6d 20 70 6c 61 6e 65 0a 66 |ass from plane.f| 00000470 61 63 65 0a 72 3d 72 61 64 69 75 73 0a 0a 4d 49 |ace.r=radius..MI| 00000480 3d 6d 6c b2 2f 33 0a 46 6f 72 20 61 20 75 6e 69 |=ml./3.For a uni| 00000490 66 6f 72 6d 20 72 6f 64 2c 20 6c 65 6e 67 74 68 |form rod, length| 000004a0 20 32 6c 3a 0a 4d 49 3d 6d 6f 6d 65 6e 74 20 6f | 2l:.MI=moment o| 000004b0 66 20 69 6e 65 72 74 69 61 20 61 62 6f 75 74 20 |f inertia about | 000004c0 61 78 69 73 20 74 68 72 6f 75 67 68 0a 63 65 6e |axis through.cen| 000004d0 74 72 65 2c 20 70 65 72 70 65 6e 64 69 63 75 6c |tre, perpendicul| 000004e0 61 72 20 74 6f 20 6c 65 6e 67 74 68 0a 6d 3d 6d |ar to length.m=m| 000004f0 61 73 73 0a 0a 4d 49 3d 6d 72 b2 0a 46 6f 72 20 |ass..MI=mr..For | 00000500 61 20 75 6e 69 66 6f 72 6d 20 68 6f 6f 70 2c 20 |a uniform hoop, | 00000510 72 61 64 69 75 73 20 72 3a 0a 4d 49 3d 6d 6f 6d |radius r:.MI=mom| 00000520 65 6e 74 20 6f 66 20 69 6e 65 72 74 69 61 20 61 |ent of inertia a| 00000530 62 6f 75 74 20 61 78 69 73 20 74 68 72 6f 75 67 |bout axis throug| 00000540 68 0a 63 65 6e 74 72 65 20 70 65 72 70 65 6e 64 |h.centre perpend| 00000550 69 63 75 6c 61 72 20 74 6f 20 70 6c 61 6e 65 0a |icular to plane.| 00000560 6d 3d 6d 61 73 73 0a 0a 4d 49 3d 6d 72 b2 2f 32 |m=mass..MI=mr./2| 00000570 0a 46 6f 72 20 61 20 75 6e 69 66 6f 72 6d 20 64 |.For a uniform d| 00000580 69 73 63 2c 20 72 61 64 69 75 73 20 72 3a 0a 4d |isc, radius r:.M| 00000590 49 3d 6d 6f 6d 65 6e 74 20 6f 66 20 69 6e 65 72 |I=moment of iner| 000005a0 74 69 61 20 61 62 6f 75 74 20 61 78 69 73 20 74 |tia about axis t| 000005b0 68 72 6f 75 67 68 0a 63 65 6e 74 72 65 20 70 65 |hrough.centre pe| 000005c0 72 70 65 6e 64 69 63 75 6c 61 72 20 74 6f 20 70 |rpendicular to p| 000005d0 6c 61 6e 65 0a 6d 3d 6d 61 73 73 0a 0a 4d 49 3d |lane.m=mass..MI=| 000005e0 32 6d 72 b2 2f 35 0a 46 6f 72 20 61 20 75 6e 69 |2mr./5.For a uni| 000005f0 66 6f 72 6d 20 73 6f 6c 69 64 20 73 70 68 65 72 |form solid spher| 00000600 65 2c 20 72 61 64 69 75 73 20 72 3a 0a 4d 49 3d |e, radius r:.MI=| 00000610 6d 6f 6d 65 6e 74 20 6f 66 20 69 6e 65 72 74 69 |moment of inerti| 00000620 61 20 61 62 6f 75 74 20 74 68 65 20 64 69 61 6d |a about the diam| 00000630 65 74 65 72 0a 6d 3d 6d 61 73 73 0a 0a 0a 0a 0a |eter.m=mass.....| 00000640 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 00000680 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |...........| 0000068b
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