Mienzaniso 7 yeMatambudziko eAngular Momentum
Kufamba Kwemakona
1. Chinhu chine nguva yekusaita basa 2 kg m2 uye inotenderera padivi rakagadzika ne kumhanya kwekona 1 rad/s. Marii? simba rekona chinhu ichocho?
Kukurukurirana
Zvinozivikanwa kuti:
Nguva yekusaita basa (I) = 2 kg m2
Kumhanya kwekona (ω) = 1 rad/s
Akabvunzwa: Mwenje wekona (L)
Mhinduro:
Fomura yeAngular momentum:
L = I ω
Tsananguro: L = angular momentum (kg m)2/s), I = nguva yekusaita basa (kg m)2), ω = kumhanya kwekona (rad/s)
Mwero wekona:
L = I ω = (2)(1) = 2 kg m2/s
2. Pulley yedhisiki yakasimba ine huremu hwe2 kg uye radius ye 0,1 metres. Kana pulley ikatenderera pa axis yayo ne 2 rad/sekondi, chii chinonzi angular momentum yepulley?
Kukurukurirana
Zvinozivikanwa kuti:
Huremu hwepureti yedhisiki yakasimba (m) = 2 kg
Nharaunda yepulley yedhisiki yakasimba (r) = 0.1 mita
Kumhanya kwekona (ω) = 2 radians/sekondi
Akabvunzwa: Kufamba kwekona kwepulley
Mhinduro:
Fomura yenguva yekusagadzikana kwediski yakasimba kana ichitenderera pane imwe axis sezvakaratidzwa mumufananidzo:
Ini = 1/2 mr2
Tsananguro: I = nguva yekusaita basa (kg m)2), m = huremu (kg), r = dhayasi (mita)
Nguva yekusashanda zvakanaka kwedhisiki rakasimba:
Ini = 1/2 (2)(0,1)2 = (1)(0,01) = 0,01 kg m2
Mwero wekona:
L = I ω = (0,01)(2) = 0,02 kg m2/s
3. Bhora rakasimba rine huremu hwe2 kg uye radius ye 0,2 metres rinotenderera rakatenderedza axis yaro nekumhanya kwe 4 rad/s. Tsvaga angular momentum yebhora rakasimba!
Kukurukurirana
Zvinozivikanwa kuti:
Huremu hwebhora rakasimba (m) = 2 kg
Nharaunda yebhora rakasimba (r) = 0,2 metres
Kumhanya kwekona (ω) = 4 radians/sekondi
Akabvunzwa: Mwenje wekona webhora rakasimba
Mhinduro:
Fomura yenguva yekusagadzikana kwebhora rakasimba kana richitenderera pane imwe axis sezvakaratidzwa mumufananidzo:
Ini = (2/5) mr2
Tsananguro: I = nguva yekusaita basa (kg m)2), m = huremu (kg), r = dhayasi (mita)
Nguva yekusagadzikana kwebhora rakasimba:
Ini = (2/5)(2)(0,2)2 = (4/5)(0,04) = 0,032 kg m2
Mwenje wekona webhora rakasimba:
L = I ω = (0,032)(4) = 0,128 kg m2/s
4. Chinhu chine huremu hwe 1 kg chinofamba mudenderedzwa chine angle velocity inogara iripo ye 2 rad/s. Sarudza angle momentum kana radius yenzira ye particle iri 10 cm.
Kukurukurirana
Zvinozivikanwa kuti:
Huremu hwechinhu (m) = 1 kg
Nharaunda yebhora rakasimba (r) = 10 cm = 10/100 = 0,1 metres
Kumhanya kwekona (ω) = 2 radians/sekondi
Akabvunzwa: Mwero wekona
Mhinduro:
Fomura yenguva yekusagadzikana kwechinhu chimwe:
Ini = Va.2 = (1)(0,1)2 = (1)(0,01) = 0,01 kg m2
Mwero wekona:
L = I ω = (0,01)(2) = 0,02 kg m2/s
Mutemo wekuchengetedza angular momentum
5. Dhisiki rakasimba rakafanana rinotanga kutenderera padivi paro nekumhanya kwe 5 rad/s. Nzvimbo yedhisiki yakaenzana nenzvimbo yakatwasuka. Huremu ne radius yedhisiki zviri 2 kg uye 0,2 metres. Kana rin'i ine huremu hwe 0,1 kg ne radius ye 0,2 metres yakaiswa pamusoro pedhisiki, uko pakati perin'i iri pamusoro pepakati pedhisiki, dhisiki nerin'i zvichatenderera pamwe chete nekumhanya kwe angle kwe…
Kukurukurirana
Zvinozivikanwa kuti:
Huremu hwesirinda yakasimba (m1) = 2 kg
Nharaunda ye silinda yakasimba (r)1) = 0,2 mamita
Kumhanya kwekona kwe silinda yakasimba (ω)1) = 5 rad/s
Huremu hwemhete (m)2) = 0,1 kg
Radiyo yeringi (r)2) = 0,2 mamita
Akabvunzwa: Kumhanya kwemakona emasilinda nemhete
Mhinduro:
Nguva yekusashanda kwe silinda yakasimba: I = 1⁄2 m1 r12 = 1⁄2 (2)(0,2)2 = (1)(0,04) = 0,04 kg m2
Nguva yekusashanda kwemhete: Ini = mr2 = (0,1)(0,2)2 = (0,1)(0,04) = 0,004 kg m2
Nguva yekusashanda kwesimbi yakasimba nerin'i (I) = 0,04 + 0,004 = 0,044 kg m2
Mwenje wekutanga wekona (L)1) = Mwendo wekupedzisira wekona (L)2)
I1 ω1 = Ini2 ω2
(0,04)(5) = (0,044)(ω)2)
(0,2) = (0,044)(ω)2)
ω2 = 0,2 : 0,044
ω2 = 4,5 rad/s
6. Mutambi weballet anotenderera maoko ake akatambanudzwa kusvika pakureba kwe150 cm uye kumhanya kwekona kwe10 radians/sekondi. Ipapo mutambi anopeta maoko ake kusvika pakureba kwe75 cm pagokora. Ndeipi kumhanya kwekona kwekupedzisira?
Kukurukurirana
Zvinozivikanwa kuti:
Nharaunda 1 (r)1) = 150 cm = 1,5 mamita
Nharaunda 2 (r)2) = 75 cm = 0,75 mamita
Kumhanya kwekona 1 (ω)1) = 10 rad/s
Akabvunzwa: Kumhanya kwekona 2 (ω)2)
Mhinduro:
Nguva yekutanga yekusagadzikana: I1 = Va.12 = (m)(1,5)2 = 2,25 XNUMX m
Nguva yekupedzisira yekusagadzikana: I2 = Va.22 = (m)(0,75)2 = 0,5625 XNUMX m
Mwenje wekutanga wekona (L)1) = Mwendo wekupedzisira wekona (L)2)
I1 ω1 = Ini2 ω2
(2,25 m)(10) = (0,5625 m)(ω)2)
22,5 m = (0,5625 m)(ω)2)
22,5 = (0,5625)(ω)2)
ω2 = 22,5/0,5625
ω2 = 40 rad/s
7. Dhisiki rakasimba rakafanana rinotanga kutenderera padivi paro nekumhanya kwemakona kwe4 rad s.-1Huremu neredhiyo yedhisiki zvinosvika 1 kg uye 0,5 m. Kana rin'i yakaiswa pamusoro pedhisiki ine huremu neredhiyo ye0,2 kg uye 0,1 m uye pakati perin'i pari pamusoro chaipo pepakati pedhisiki yakasimba, ipapo dhisiki yakasimba nerin'i zvichatenderera pamwe chete nekumhanya kwekona...
A. 1 rad/s
B. 2 rad/s
C. 3 rad/s
D. 4 rad/s
E. 5 rad/s
Kukurukurirana :
Nguva yeInertia sirinda yakasimba : I = ½ mr2 = ½ (1 kg)(0,5 m)2 = (0,5)(0,25) = 0,125 kg m2
Nguva yeKusasimba kwemhete: Ini = mr2 = (0,2 kg)(0,1 m)2 = (0,2)(0,01) = 0,002 kg m2
Kumhanya Kwekutanga Kwekona (L)1) = Kumhanya Kwekupedzisira Kwekona (L)2)
I1 ω1 = Ini2 ω2
(0,125 kg m2)(4 rad/s) = (0,125 kg m2 + 0,002 kg m2)(ω)2)
(0,5) = (0,127)(ω)2)
ω2 = 0,5 : 0,127
ω2 = 4 rad/s
Mhinduro chaiyo ndiD.
