Mehlala e 7 ea Mathata a Angular Momentum
Motsotso o Angular
1. Ntho e na le motsotso oa ho se inertia 2 kg m2 'me e potoloha holim'a axis e tsitsitseng ka lebelo la angular Rad/s e le 1. Ke bokae? lebelo la angular ntho eo?
Puisano
Hoa tsebahala hore:
Motsotso oa ho se inertia (I) = 2 kg m2
Lebelo la Angular (ω) = 1 rad/s
O botsitse: Motsamao o motsu (L)
Karabo:
Foromo ea momentum ea angular:
L = Ke ω
Tlhaloso: L = momentum ea angular (kg m)2/s), I = motsotso oa ho se inertia (kg m2), ω = lebelo la angular (rad/s)
Motsamao oa angular:
L = I ω = (2)(1) = 2 kg m2/s
2. Pulley e tiileng ea disc e na le boima ba 2 kg le radius ea limithara tse 0,1. Haeba pulley e potoloha mothating oa eona ka lebelo le sa fetoheng la angular la 2 rad/motsotsoana, lebelo la angular la pulley ke lefe?
Puisano
Hoa tsebahala hore:
Boima ba pulley ea disc e tiileng (m) = 2 lik'hilograma
Radius ea pulley ea disc e tiileng (r) = 0.1 meter
Lebelo la Angular (ω) = 2 radians/motsotsoana
O botsitse: Motsamao o potolohang oa pulley
Karabo:
Foromo ea motsotso oa inertia oa disc e tiileng haeba e potoloha holima axis joalo ka ha ho bontšitsoe setšoantšong:
Ke = halofo ea monghali2
Tlhaloso: I = motsotso oa ho se inertia (kg m)2), m = boima (kg), r = radius (limithara)
Nako ea ho se sebetse hantle ha diski e tiileng:
Ke = 1/2 (2)(0,1)2 = (1)(0,01) = 0,01 kg m2
Motsamao oa angular:
L = I ω = (0,01)(2) = 0,02 kg m2/s
3. Bolo e tiileng e boima ba 2 kg le radius ea limithara tse 0,2 e potoloha ho potoloha axis ea eona ka lebelo la angular la 4 rad/s. Fumana momentum ea angular ea bolo e tiileng!
Puisano
Hoa tsebahala hore:
Boima ba bolo e tiileng (m) = 2 kg
Radius ea selika se tiileng (r) = limithara tse 0,2
Lebelo la Angular (ω) = 4 radians/motsotsoana
O botsitse: Motsamao o motsu oa selika se tiileng
Karabo:
Foromo ea motsotso oa inertia oa bolo e tiileng haeba e potoloha holima axis joalo ka ha ho bontšitsoe setšoantšong:
Ke = (2/5) monghadi2
Tlhaloso: I = motsotso oa ho se inertia (kg m)2), m = boima (kg), r = radius (limithara)
Motsotso oa ho se tsitse ha selika se tiileng:
Ke = (2/5)(2)(0,2)2 = (4/5)(0,04) = 0,032 kg m2
Motsamao o motsu wa sedikadikwe se tiileng:
L = I ω = (0,032)(4) = 0,128 kg m2/s
4. Ntho e boima ba 1 kg e tsamaya ka sedikadikwe ka lebelo le sa fetoheng la 2 rad/s. Fumana momentum ya angular haeba radius ya tsela ya karoloana e le 10 cm.
Puisano
Hoa tsebahala hore:
Boima ba ntho (m) = 1 kilograma
Radius ea selika-likoe se tiileng (r) = 10 cm = 10/100 = 0,1 metres
Lebelo la Angular (ω) = 2 radians/motsotsoana
O botsitse: Motsamao o potolohang
Karabo:
Foromo ea motsotso oa inertia ea karoloana:
Ke = Monghali.2 = (1)(0,1)2 = (1)(0,01) = 0,01 kg m2
Motsamao oa angular:
L = I ω = (0,01)(2) = 0,02 kg m2/s
Molao oa paballo ea motsamao oa angular
5. Disiki e tiileng e ts'oanang e potolohang qalong moleng oa eona ka lebelo la angular la 5 rad/s. Sepakapaka sa disk se bapile le sefofane se bataletseng. Boima le radius ea disk ke 2 kg le 0,2 metres. Haeba lesale le nang le boima ba 0,1 kg le radius ea 0,2 metres le behiloe holim'a disk, moo setsi sa lesale se leng ka holimo ho setsi sa disc, disc le lesale li tla potoloha hammoho ka lebelo la angular la…
Puisano
Hoa tsebahala hore:
Boima ba silindara e tiileng (m1) = 2 lik'hilograma
Radius ea silindara e tiileng (r)1) = limithara tse 0,2
Lebelo le potolohang la silindara e tiileng (ω1) = 5 rad/s
Boima ba lesale (m2) = 0,1 lik'hilograma
Radiyo ya lesale (r)2) = limithara tse 0,2
O botsitse: Lebelo la li-cylinder le masale a manehang
Karabo:
Nako ea ho se sebetse hantle ha silindara e tiileng: I = 1⁄2 m1 r12 = 1⁄2 (2)(0,2)2 = (1)(0,04) = 0,04 kg m2
Motsotso oa ho se tsitse ha lesale: Ke = monghali2 = (0,1)(0,2)2 = (0,1)(0,04) = 0,004 kg m2
Nako ea ho se sebetse ha silindara e tiileng le lesale (I) = 0,04 + 0,004 = 0,044 kg m2
Motsamao oa pele oa angular (L)1) = Momentum oa ho qetela oa angular (L2)
I1 ω1 = KE2 ω2
(0,04)(5) = (0,044)(ω)2)
(0,2) = (0,044)(ω2)
ω2 = 0,2 : 0,044
ω2 = 4,5 rad/s
6. Motantshi wa ballet o a dikologa matsoho a hae a otlolohile ho fihlela bolelele ba 150 cm le lebelo la angular la di-radian tse 10 ka motsotsoana. Ebe motantshi o mena matsoho a hae ho fihlela bolelele ba 75 cm ka setsoe. Lebelo la ho qetela la angular ke lefe?
Puisano
Hoa tsebahala hore:
Radius 1 (r)1) = 150 cm = 1,5 limithara
Radius 2 (r)2) = 75 cm = 0,75 limithara
Lebelo la Angular 1 (ω1) = 10 rad/s
O botsitse: Lebelo la Angular 2 (ω2)
Karabo:
Motsotso oa pele oa inertia: I1 = Monghali.12 = (m)(1,5)2 = 2,25 limithara
Motsotso oa ho qetela oa ho se inertia: I2 = Monghali.22 = (m)(0,75)2 = 0,5625 limithara
Motsamao oa pele oa angular (L)1) = Momentum oa ho qetela oa angular (L2)
I1 ω1 = KE2 ω2
(2,25 m)(10) = (0,5625 m)(ω)2)
22,5 m = (0,5625 m)(ω2)
22,5 = (0,5625)(ω2)
ω2 = 22,5/0,5625
ω2 = 40 rad/s
7. Disiki e tiileng e nang le sebopeho se ts'oanang e qala ho potoloha hodima axis ya yona ka lebelo le ka lehlakoreng la 4 rad s.-1Boima le radius ea disk ke 1 kg le 0,5 m. Haeba lesale le behiloe holim'a disk e nang le boima le radius ea 0,2 kg le 0,1 m 'me setsi sa lesale se le kaholimo ho setsi sa disk e tiileng e silindara, joale disk e tiileng e silindara le lesale li tla potoloha hammoho ka lebelo le potolohang...
A. 1 rad/s
B. 2 rad/s
C. 3 rad/s
D. 4 rad/s
E. 5 rad/s
Puisano :
Motsotso oa Bofokoli silindara e tiileng: I = ½ mr2 = ½ (1 kg)(0,5 m)2 = (0,5)(0,25) = 0,125 kg m2
Motsotso oa Boima ba lesale: Ke = monghali2 = (0,2 kg)(0,1 m)2 = (0,2)(0,01) = 0,002 kg m2
Motsotso oa Angular oa Pele (L)1) = Momentum ea ho Qetela ea Angular (L)2)
I1 ω1 = KE2 ω2
(0,125 kg m2)(4 rad/s) = (0,125 kg m2 + 0,002 kg m2)(ω2)
(0,5) = (0,127)(ω2)
ω2 = 0,5 : 0,127
ω2 = 4 rad/s
Karabo e nepahetseng ke D.
