Mono no Ugoki

Maegaki

Tikara to undô no kankei o siraberu gakumon wa "rikigaku" to yobare, buturigaku no mottomo kihon to naru gakumon de aru.
Rikigaku no sugureta kyôkasyo wa takusan kakarete ori, mata Rômazi de kakareta Tamaru-Takurô Sensei no rikigaku no kyôkasyo wa kiwamete sugureta mono to site nadakai mono de aru.
Sore wa
Rikigaku no Kyôkwasyo . . . . . Nippon-no-Rômazi-Sya
RIKIGAKU I, RIKIGAKU II . . . . . . . Iwanami Syoten
de aru.
Kono tabi, sara ni Rômazi de "rikigaku" o kaite miru no wa tugi no yô na wake kara de aru.
Kono kakimono wa Rômazi de kaite aru ue, sukunai kotonari tango de kaku yô ni tutomete iru. Kore wa omo ni tugi no yô na nerai kara de aru.
1. Hito wa kotoba de kangaete iru. Kotoba to kotoba o tugitugi to tunaide yuku no ga, kangaeru to iu koto de aru. To suru to, sukunai tango de kangaeru koto wa, sukunai ômoto no kangae kara suzimiti o tatete kangaeru koto ni naru no de wa nakarô ka?
mata
2. Rômazibun o yomu no ni, sukunai tango no katati de sumu kara, sugu nareru no de wa nai ka?
3. Nippon umare de nai hito ga, Nippongo o sukosi sitte iru dake de yomeru kakimono ni naru no de wa nakarô ka?
to iu no mo mô hitotu no nerai de aru.
Kono yô na kokoromi na no de, nakami ni tuite wa motiron, kotoba zukai ya iimawasi nado ni tuite no "arasagasi" o hiroku onegai sitai
Nao,kono bun de wa atarasii kikinarenai kotoba o tukatta tokoro mo aru. Kizuita tokoro de wa, "hutû ni tukawarete iru kotoba ya, eigo o kakko ( ) no naka ni oginatte iru.

Simizu-Masayuki




1. Ugoki ni tuite no kimari 1

1.1 Hi no nai tokoro ni kemuri wa tatanai
"Hi no nai tokoro ni kemuri wa tatanai", to iu kotoba ga aru. Nani mo nai tokoro ni wa nani mo okoranai, to iu imi de arô.
Kami ya Hotoke, aruiwa Kirisuto no osie o sinzite iru hito ga aru. Monogoto ga "dono yô ni site" okotte iru no ka, o sirabete iru hito ni site mo, minna nani ka o sinzite iru. Hotoke o sinzite iru hito mo aru si, Kirisuto o sinzite iru hito mo aru. Sikasi,"dono yô ni site" okotte iru ka o sirabete iru hito wa
"Kono yo no naka de okoru koto wa
minna aru [kimari] ni sitagatte iru",
to iu koto dake wa, minna ga sinzite iru koto de aru.
Kono kimari wa Kami ga tukutta mono ka, dare ga tukutta mono ka wa wakaranai ga, hito ga tukuttari, kimetari sita mono de wa nai mono de aru.
Ooku no hito ga sinzite iru itiban moto ni naru koto wa nani de arô ka?
"Nani mo nai tokoro ni wa nani mo okoranai!"
to iu koto de wa nakarô ka?

1.2 Ugokanai mono
Mawari o miru to, ugoite iru mono mo aru ga ugoite inai mono mo aru. Ugoite inai arisama o "tomatte iru" to iu. Tomatte iru arisama mo, ugoite iru arisama no tokubetu no baai da to kangaeru koto ga dekiru.
"Nani mo nai tokoro ni wa nani mo okoranai!", to iu koto o "tomatte iru mono" ni atehameru to dô naru ka?
"Tomatte iru mono ni, nani mo sinakereba tomatte iru.", to iu koto ni naru. Hantai ni, "tomatte ita mono" ga ugokidasita to suru to, ugokasu tame ni nani ka sita ni tigainai. Tomatte iru mono o ugokasu "nani ka" o "ugokasi (ryokuseki,impulse)" to iu. Kono ugokasi wa, me ni mieru mono de wa nai si, katati mo nai rasii.
"Tomatte iru mono ni nani mo sinakareba tomatte iru", to iu koto o, "ugokasi" to iu kotoba o tukatte, suzimiti o hikkurikaesite iu to tugi no yô ni naru.
"Tomatte iru mono ni,
ugokasi ga hatarakanai nara,
itu made mo tomatte iru."

1.3 Ugoite iru mono
Tugi ni, ugoite iru mono o kangaeru.
Ugoite iru, to itte mo "higasi muki" ni ugoitari, "minami muki" ni ugoitari to iu yô ni, "muki" (direction) ni yotte tigau. Mata, onazi muki ni ugoite ite mo, onazi 1 byô no aida ni tôku hanaretari, sukosi hanaretari, to iu hû ni "ôkisa" no tigai mo aru.
Ugoite iru toki no ryô (quantity) o muki to ôkisa o hikkurumete "ugoki no ryô", "ugoki-ryô" aruiwa kantan ni "ugoki" (undôryô, momenta) to iu.
Ugoki no yô ni, "muki to ôkisa" o motu ryô o "muki-ryô" (vector) to iu.
Kore ni taisite, "ôkisa" dake no ryô o "ôkisa-ryô" (scalar) to iu.
Tatoeba, nagasa, hirosa, kasa (taiseki, volume) nado wa "ôkisa-ryô" de ari, iti-gawari (hen'i, displacement), ugoki nado ga "muki-ryô" de aru.
Ugoite iru mono ni nani mo sinai de ite mo itu ka wa tomatte simau koto ga ôi. Sikasi, sugu tomaru koto mo areba, nakanaka tomaranai koto mo aru. "Nani mo nakereba nani mo okoranai", to iu kangae o atehamete kangaeru to, "ugoite iru mono ga tomaru no wa nani ka ga aru kara" ni tigai nai. "Tomatte iru mono" o ugokasu no ga "ugokasi" de aru nara, "ugoite iru mono o tomeru" no mo "ugokasi" de arô. To suru to, tugi no yô ni kangaeru no ga itiban sunao na koto de arô.
"Ugoite iru mono ni,
ugokasi ga hatarakanai nara,
itu made mo ugoki wa onazi de aru"

1.4 Ugoki no dai iti no kimari
1.2 to 1.3 de nobeta koto wa, kantan ni iu to, "ugoite ite mo, tomatte ite mo nani mo sinai nara sono mama no arisama ga tuzuku" to iu koto de aru.
Mô sukosi erasô ni iu to
"Mono ni ugokasi ga hatarakanai nara, ugoki wa kawaranai."
to iu koto de aru. Kore o "Ugoki no dai iti no kimari" to iu. Mata, kono imi o totte "Sono mama no kimari" (kansei no hôsoku, law of inertia) to mo iu.
Dai iti no kimari de wa, "ugokasi ga nai" toki no koto o itte iru wake de aru. "Tomatte iru" toki wa ugoite inai no de "ugoki ga 0" de aru. Itu made mo ugoki ga 0 de ari, tomatte iru to iu koto de aru. Ugoite iru toki wa, "ugoki" wa kawaranai. Ugoki ni wa "muki" to "ôkisa" ga aru. "Muki ga kawaranai" to iu koto wa, onazi muki ni "massugu" ugoku to iu koto de aru. "Ooisa ga kawaranai" to iu koto wa ugokikata ga onazi to iu koto de aru. 1 byô ni 1 cm no wariai de ugoite ita no nara, itu made mo 1 byô ni 1 cm no wariai de ugoku to iu koto de aru.

1.5 Ugoki no dai iti no kimari wa, nani o kimeta ka?
"Ugokasi (ryokuseki) ga nai nara, ugoki (undôryô) ga kawaranai", to iu no ga dai iti no kimari de aru. Kore wa kore de kitin to sita imi o motte iru ga, kono kimari no naka ni wa ikutu ka no ômoto ni naru kangae ga aru koto ni me o mukeru koto ga taisetu de aru.
"Tomatte iru", to iu koto wa "toki ga tatte mo, iti ga kawaranai",to iu koto de aru. Koko ni "toki" to "iti" to iu hutatu no kangae ga umarete iru. "Toki" ya "iti" ni tuite no kangae ni wa, iroiro na kangaekata ga aru ga, Newton wa tugi no yô ni kangaete iru no de aru.
Kono yo ni wa "tadasii toki" (zettai zikan) to iu mono ga aru. Zutto hurui mukasi kara, zutto saki made "tadasii toki" to iu mono ga subete no iti de onazi yô ni susunde iru, to iu no de aru. Arappoi iikata o suru to, "tadasii toki" ni awaseta tadasii tokei ga arayuru iti ni aru, to iu koto de aru.
Koko no iti, asoko no iti to iu yô ni iroiro na iti ga aru. Kono yo no iti (position) o subete hikkurumete "hirogari" (kûkan, space) to iu. Subete no iti ga tomatte iru yô na hirogari ga aru. Sono ue, ugokasi ga nai toki ni wa ugoki ga kawaranai no de aru kara, tatoeba 1 byô ni tuite no iti-gawari ga onazi nagasa ni naru yô na "tadasii hirogari" (zettai kûkan) to iu mono ga aru to iu no ga Newton no kangae de aru.
Kono yô ni kangaeru to, dai iti no kimari to iu no wa, "ugokasi ga nai toki ni wa ugoki wa kawaranai" to iu koto o itte iru ga, betu no mikata o suru to "tadasii toki" to "tadasii hirogari" to iu mono o kimeta mono de mo aru.

2 Ugoki no Kimari 2
2.1 Ugoki to hayasa

Mazu,hitotu no mono ni tuite kangaeru. Kono toki, "ugoki" wa ugokikata --- ugoku muki to ôkisa --- dake de kimaru hazu de aru. "Ugoku ôkisa" no koto o "hayasa" (hayasa, sokudo) to iu. Kihon no hakarikata de iu to, 1 byô [s] ni ugoku nagasa [m] no koto de aru kara, hayasa no kizami (tan'i, unit) wa [m/s] de aru.
"Ugoku muki to ôkisa" o issyo ni site "muki-ryô hayasa" (sokudo vector) to iu. Ookisa-ryô no "hayasa" to matigaeru osore no nai toki ni wa kantan ni "hayasa" to itte mo yoi. Kore kara [hayasa v] no yô ni, muki-ryô wa "[ ]" de kakonde kaku koto ni suru.
Kore made "ugoki" to itte kita mono wa, hayasa [v] to onazi muki o motte ori, mata, hitotu no mono de wa,sono ôkisa wa hayasa v ga kimaru to kimatte kuru. Tumari, ôkisa wa "v" no kakawari (kansû, function) de aru.
Sitagatte, [ugoki P] wa
[ugoki P] = f(v) [v] ............................. (2.1)
no yô ni kaku koto ga dekiru. Koko made wa "kangae no suzimiti" de aru ga, kono kakawari f(v) ga donna mono de aru ka, wa "kono yo no kimari" de atte rikutu dake de wakaru mono de wa nai. Kore ga hitotu no kimatta atai de aru koto o mituketa no ga Newton de atta. Kono atai o "k" to kaku to
[ugoki P] = k [v] ...................................... (2.2)
to kaku koto ga dekiru to iu no de aru.
Kono "k" wa ittai donna mono de arô ka?

2.2 Ugokasi to mono-ryô
Tomatte iru mono ni, "ugokasi" o ataeru to ugoku. Tomatte iru arisama wa, [ugoki 0] to kaite mo yoi si, "nai ugoki" to iu imi de "nani mo kakanai" koto ni site mo yoi. Soko de, aru ugokasi [ugokasi G] o ataeru to, [ugoki P] to iu ugoki ni naru koto o siki de
[ugoki 0] + [ugokasi G] ==> [ugoki P]
to kaku koto mo dekiru si, mata
[ugokasi G] ==> k [v] ....................................... (2.3)
to kaku koto mo dekitu. Sara ni, "ugokasi" no kizami (tan'i) o umaku tukuru to
[ugokasi G] = k [v] ............................................ (2.4)
to kaku koto mo dekiru.
Sate, koko ni hontô ni onazi mono ga hutatu aru to siyô. Tatoeba, hontô ni, onazi yô ni dekita tama A, B ga aru to suru. Hutatu tomo, hazime wa tomatte ite, sorezore ni [ugokasi G] o ataete sorezore ga [ugoki G] no arisama ni natta to suru.
Siki de kaku to
A ni tuite: [ugokasi G] = k [v] ........................... (2.5)
B ni tuite: [ugokasi G] = k [v] ................................ (2.6)
to naru.
Motomoto wa hutatu no mono de atta ga, kono hutatu no tama ga "me ni mienai ito" de tunagatte iru hitotu no mono to kangaeru to, [ugokasi] wa sorezore ni ataeru kara
[ugokasi G] + [ugokasi G] = 2k [v]
to naru. Mittu areba, "ugokasi" wa 3 bai ni naru si, "ugoki" mo [v] no 3k bai ni naru. Yottu areba, "ugokasi" mo 4 bai ni naru si, "ugoki" wa [v] no 4k bai ni naru. ...

Ikutu ka aru toki, zenbu o hitotu no mono to kangaeru to
[ugokasi zenbu] = [ugoki zenbu] .......................... (2.7)
Koko de
[ugokasi zenbu] = [ugokasi G] x (mono no kazu) ....................... (2.8)
[ugoki zenbu] = (mono no kazu) k [v] ................................. (2.9)
to naru.
Siki (2.9) ni arawareta "(mono no kazu) x k" wa nani o arawasite iru ka?
Mono no kazu ga, 2 ko, 3 ko, 4 ko, ... to naru ni turete, 2k, 3k,4k, ... to natta no de aru kara, aru imi de no "mono no ryo" no ôi, sukunai o arawasu ryô de aru.
Kono imi de, kore o "mono-ryô" (situryô, mass) to ii, "m" to kaku koto ga ôi. Sunawati, mono-ryô m wa
m = k x (mono no kazu) ................................... (2.10)
Mono no ryô o arawasu hôhô ni wa, iroiro na hôhô ga aru. Korera ga donna tokutyô o motte iru ka, mata "k" ya "m" ga donna imi o motte iru ka, motto horisagete kangaeru koto ni siyô.

2.3 Mono no ôkisa to mono-ryô
Mono ga ôkii, tiisai to ka, ôi, sukunai to ka iu koto ga aru. Dotira mo aru imi de, mono no ryô o iu kotoba de aru.
"Ookii, tiisai" to iu no wa, "hirogarikata" no ôkisa o iu koto ga ôi. Mono no ryô no "ôi, sukunai" o hakaru toki mo, kimatta iremono de "nanbai aru ka" de hakaru koto ga ôkatta. Tatoeba, kome ya mugi no ryô o hakaru toki ni mo, "issyô masu" (1.8 L hairu iremono) de nanbai aru ka, to iu hakarikata o site kita. Tumari, mono no ryô o hakaru no ni mo, mono no kasa (taiseki) de hakatta no de aru.
Tokoro ga, issyô masu ni kome o irete oite mo, kore o sibaraku yuri-ugokasu to sukosi sukima ga dekite kuru no de, motto hairu yô ni naru. Mugi-ko nado o hakaru to, motto tigai ga dete kuru. Hazime masu ni ippai irete oite mo, sikkari ositukeru to motto hairu yô ni naru. Mono no ryô wa "kasa" de wa tadasiku kimerarenai wake de aru. Mono no ryô wa dô sureba kitin to kimeru koto ga dekiru no de arô ka?
Subete no mono wa "monokko" (bunsi) kara dekite iru. Subete no mono ga sore izyô wakeru koto ga dekinai "kakera" kara dekite iru to iu kangae wa, huruku Kigen 4-5 hyakunen mae no Girisya tetugaku ya Indo tetugaku ni sono moto o miru koto ga dekiru ga, imadoki de wa mohaya utagai no nai kotogara de aru. Kono moto ni naru kakera o "monokko" to iu no de aru. Sitagatte, mono no ryô wa "monokko no kazu" de kitin to kimeru koto ga dekiru.

Mae no setu no siki
m = (mono no kazu) x k ................................... (2.10)
no naka no "k" no atai o "monokko hitotu no mono-ryô" to sureba, "mono-ryô m" wa "monokko hitotu no mon-ryô ni monokko no kazu o kaketa mono" de atte, mono no ryô o kimeru ryô sono mono de aru koto ga wakaru. Kore ga "m" o "mono-ryô" to nazuketa iware de aru.
Tatoeba, mizu 1 L (rittoru) to tetu 1 L to dotira ga ôi ka, to iu koto wa imi o motte inai. Tokoro ga, mae no setu de mitibiita "mono-ryô m" wa "mono no ugokikata" kara kimeta mono de aru kara, "mono-ryô to site dotira ga ôi ka" o iu koto ga dekiru no de aru. Onazi monokko kara dekite iru hutatu no mono de wa, mono-ryô ga 2 bai de aru koto wa monokko no kazu ga 2 bai de aru koto o simesite iru. Mata, onazi monokko kara dekita mono de mo, tigau monokko kara dekita mono de mo, monôryô ga 2 bai de aru koto wa onazi ugokasikata o suru tame ni 2 bai no "ugokasi" ga iru koto o simesite iru koto ni naru.
Kono yô ni, "monôryô" wa hontô no imi de no "mono no ryô" o arawasu ryô de aru to tomo ni, "mono no ugokikata" no seisitu o simesu ryô de mo aru koto ga wakaru.
Sate, monokko to iu mono wa totemo tiisai mono de aru. Tatoeba mizu no monokko hitotu no mono-ryô "k" wa totemo tiisai ryô de aru. Soko de, hutû ni tukaiyasui teido no ôkisa o totte "1 kg" to iu mono-ryô no kizami ga kimerarete iru. 1 kg wa oyoso mizu 1 L no mono-ryô de aru.

2.4 Ugoki no dai ni no kimari --- Ugoki-ryô no kimari
Mae no setu to sono mata mae no setu to de nobeta koto o matomete miyô.
Mono ga ugoku to iu koto wa, muki to ôkisa o motta ryô de, ugoki-ryô (undôryô, momenta) to iu. Ugoki-ryô wa mono-ryô to muki-ryô hayasa [v] o kaketa mono de aru.
[ugoki-ryô] = (mono-ryô) x [mukiryô hayasa] ...................... (2.11)
Ugokikata o kaeru koto, iikaeru to [ugoki-ryô] o kaeru ni wa sono moto ni naru "aru mono" ga aru. Kore mo "mukiryô" de atte, "ugokasi-ryô" aruiwa kantan ni "ugokasi" (impulse) to iu.
Kô site, [ugoki-ryô A1] no mono ni [ugokasi-ryô G] o ataeru to [ugoki-ryô A2] no arisama ni naru. Siki de kaku to
[ugoki-ryô A1] + [ugokasi-ryô G] = [ugoki-ryô A2] ................. (2.12)
Mata, [ugoki-ryô 1] o migi-gawa ni utusite
[ugokasi-ryô G] = [ugoki-ryô A2] - [ugoki-ryô A1] ................. (2.13)
to kaku koto mo dekiru.
Siki (2.13) no migi-gawa no yô ni, "ato no ryô" kara "hazime no ryô" o hiita mono wa "hueta ryô" de aru. Sitagatte, (2.13) no migi-gawa wa [ugoki-ryô] no huedaka de aru.
Siki (2.13) wa tugi no yô ni iu koto ga dekiru.
"Mono ni [ugokasi] o ataeru to sore dake [ugoki-ryô] ga hueru." ......................... (2.14)
Kore o "Ugoki no dai ni no kimari" to iu. Mata kono imi o totte "Ugoki-ryô no kimari" to mo iu.
Kore de "mono no ugokikata no kimari" o mitibiite kita yô de aru ga, zitu wa nakami wa mada hotondo kimatte inai no de aru. [ugoki-ryô] ni tuite wa kitin to kimatta wake de aru ga, kore o kaeru tame ni wa, [ugokasi-ryô] to iu "nani ka" ga hituyô da, to iu dake de aru. Kore ga tugi no mondai de aru.

***** Tuzuku *****