Dokar kiyaye ƙarfin kusurwa ya bayyana cewa idan lokacin ƙarfi da ya biyo baya a cikin abu mai tauri wanda ke juyawa ƙimar sifili ce to ƙarfin kusurwa Abu mai tauri a cikin motsi mai juyawa akai-akai. Ana iya samo dabarar dokar kiyaye motsin kusurwa ta hanyar lissafi ta hanyar gyara dabarar dokar motsi ta biyu ta Newton don motsin kusurwa.
Wannan sigar motsi mai kusurwa ta dokar Newton ta biyu kwatancen juyawa ne na dabarar Sigar doka ta biyu ta Newton ta hanzari.
Idan lokacin ƙarfin da aka samu ya zama sifili, dabarar da ke sama ta canza zuwa:
Bayani:
Misalin matsalar:
1. Ƙwayar da ke cikin motsi na juyawa tana da lokacin inertia na 4 kg m2 da kuma saurin kusurwa na 2 rad/s. Idan saurin kusurwa na barbashi ya canza zuwa 4 rad/s to lokacin inertia na barbashi ya canza zuwa…
Tattaunawa
An sani :
Lokacin farko na inertia = 4 kg m2
Saurin kusurwa na farko = 2 rad/s
Gudun kusurwa na ƙarshe = 4 rad/s
An tambaya : lokacin ƙarshe na rashin ƙarfi?
Jawab :
Dokar kiyaye ƙarfin kusurwa ta bayyana cewa:
Motsin kusurwa na farko (L)o) = ƙarfin kusurwa na ƙarshe (Lt)
(lokacin farko na inertia) (gudun kusurwa na farko) = (lokacin ƙarshe na inertia) (gudun kusurwa na ƙarshe)
(4 kg m2)(2 rad/s) = (lokacin ƙarshe na inertia)(4 rad/s)
Lokacin ƙarshe na inertia = 2 kg m2
2. Ƙwayar da nauyinta ya kai kilogiram 2 tana juyawa a kusa da axis na juyawa daga nisan mita 2 tare da saurin kusurwa na 2 rad/s. Idan nisan ƙwayar daga axis na juyawa ya canza zuwa mita 1, a ƙayyade saurin kusurwa na ƙwayar!
Tattaunawa
An sani :
Nauyin barbashi = 2 kg
Nisa daga barbashi daga axis na juyawa (1) = mita 2
Saurin kusurwa na farko = 2 rad/s
Nisa daga barbashi daga axis na juyawa (2) = mita 1
An tambaya : saurin kusurwa na ƙarshe?
Jawab :
Lissafa lokacin inertia (I) na barbashi
Lokacin farko na inertia (I) farawa) :
I farawa = Mr.2 = (2 kg)(2 m)2 = (kilogiram 2)(4 m2) = 8 kg m2
Lokacin ƙarshe na inertia (I) karshen) :
I karshen = Mr.2 = (2 kg)(1 m)2 = (2 kg)(1 m)2) = 2 kg m2
Lissafin saurin kusurwa na ƙarshe
Dokar kiyaye ƙarfin kusurwa :
Motsin kusurwa na farko = motsin kusurwa na ƙarshe
(lokacin farko na inertia) (gudun kusurwa na farko) = (lokacin ƙarshe na inertia) (gudun kusurwa na ƙarshe)
(8 kg m2)(2 rad/s) = (2 kg m2)(gudun kusurwa na ƙarshe)
Gudun kusurwa na ƙarshe = 8 rad/s
3. Faifan silinda mai kama da juna yana juyawa da farko a kan axis ɗinsa tare da saurin kusurwa na 4 rad/s. Girma da radius na faifan sune kilogiram 1 da mita 0,5. Lokacin da faifan ke juyawa, ana sanya zobe mai nauyi da radius na mita 0,2 da 0,1 a saman faifan don faifan da zoben su juya tare. Tsakiyar zoben yana kai tsaye sama da tsakiyar faifan. A tantance saurin kusurwa na faifan da zoben!
Tattaunawa
An sani :
Saurin kusurwa na farko = saurin kusurwa na silinda mai ƙarfi = 4 rad/s
Nauyin silinda mai ƙarfi = 1 kg
Radius na silinda mai ƙarfi = mita 0,5
Nauyin zoben = 0,2 kg
Radius na zobe = mita 0,1
An tambaya : gudun kusurwa na ƙarshe = saurin kusurwa na zobe da silinda mai ƙarfi?
Jawab :
Tsarin lokacin inertia na silinda mai kama da juna = I = ½ mr2
Tsarin lokacin inertia na zobe = I = mr2
Lokacin farko na inertia = lokacin inertia na silinda mai ƙarfi:
Ni = ½ mr2 = ½ (kilogiram 1)(mita 0,5)2 = (kilogiram 0,5)(0,25 m2) = 0,125 kg m2
Lokacin ƙarshe na inertia = lokacin inertia na silinda mai ƙarfi + lokacin inertia na zobe:
Lokacin inertia na zoben = I = mr2 = (0,2 kg)(0,1 m)2 = (kilogiram 0,2)(0,01 m2) = 0,002 kg m2
Lokacin ƙarshe na inertia = 0,125 kg m2 + 0,002 kg m2 = 0,127 kg m2
Dokar kiyaye ƙarfin kusurwa :
Motsin kusurwa na farko (L)o) = ƙarfin kusurwa na ƙarshe (Lt)
(lokacin farko na inertia) (gudun kusurwa na farko) = (lokacin ƙarshe na inertia) (gudun kusurwa na ƙarshe)
(0,125 kg m2)(4 rad/s) = (0,127 kg m2)(gudun kusurwa na ƙarshe)
0,5 kg m2/s = (0,127 kg m2)(gudun kusurwa na ƙarshe)
Gudun kusurwa na ƙarshe = 0,5 / 0,127
Gudun kusurwa na ƙarshe = 4 rad/s
