Mafunso a chitsanzo cha angular momentum

Zitsanzo 7 za Mavuto a Angular Momentum

Mphamvu Yozungulira

1. Chinthu chili ndi mphindi ya kutopa 2 kg m² ndipo imazungulira pa mzere wokhazikika ndi liwiro la angular 1 rad/s. Ndalama zingati? mphamvu ya angular chinthu chimenecho?
Zokambirana
Amadziwika kuti:
Nthawi ya kulephera (I) = 2 kg m²
Liwiro la angular (ω) = 1 rad/s
Anafunsa kuti: Mphamvu ya angular (L)
Yankho:
Fomula ya angular momentum:
L = Ine ω
Kufotokozera: L = angular momentum (kg m)²/s), I = mphindi ya kusakhala ndi mphamvu (kg m²), ω = liwiro la angular (rad/s)
Mphamvu ya angular:
L = I ω = (2)(1) = 2 kg m²/s

2. Pulley yolimba ya disc imakhala ndi kulemera kwa 2 kg ndi radius ya 0,1 metres. Ngati pulley imazungulira pa axis yake ndi liwiro lokhazikika la 2 rad/sekondi, kodi mphamvu ya angular ya pulley ndi yotani?
Zokambirana
Amadziwika kuti:
Kulemera kwa pulley yolimba ya disc (m) = 2 kg
Ulalo wa pulley ya disc yolimba (r) = 0.1 mita
Liwiro la angular (ω) = ma radians awiri/sekondi
Anafunsa kuti: Mphamvu ya angular ya pulley
Yankho:
Fomula ya mphindi ya inertia ya diski yolimba ngati ikuzungulira pa mzere monga momwe chithunzichi chikusonyezera:
Ine = 1/2 mr²
Kufotokozera: I = mphindi ya inertia (kg m)²), m = kulemera (kg), r = utali wozungulira (mita)
Nthawi ya kusakhazikika kwa diski yolimba:
Ine = 1/2 (2)(0,1)² = (1)(0,01) = 0,01 kg m²

Mphamvu ya angular:
L = I ω = (0,01)(2) = 0,02 kg m²/s

3. Mpira wolimba wolemera makilogalamu awiri ndi utali wa mamita 0,2 umazungulira mozungulira mzere wake ndi liwiro la 4 rad/s. Dziwani mphamvu ya angle ya mpira wolimba!
Zokambirana
Amadziwika kuti:
Kulemera kwa mpira wolimba (m) = 2 kg
Ulalo wa bwalo lolimba (r) = mamita 0,2
Liwiro la angular (ω) = ma radians awiri/sekondi
Anafunsa kuti: Mphamvu ya angular ya bwalo lolimba
Yankho:
Fomula ya mphindi ya inertia ya mpira wolimba ngati ukuzungulira pa mzere monga momwe chithunzichi chikusonyezera:
Ine = (2/5) mr²
Kufotokozera: I = mphindi ya inertia (kg m)²), m = kulemera (kg), r = utali wozungulira (mita)
Nthawi ya inertia ya bwalo lolimba:
Ine = (2/5)(2)(0,2)² = (4/5)(0,04) = 0,032 kg m²

Mphamvu ya angular ya mpira wolimba:
L = I ω = (0,032)(4) = 0,128 kg m²/s

4. Chinthu cholemera makilogalamu 1 chimayenda mozungulira ndi liwiro lokhazikika la 2 rad/s. Dziwani mphamvu ya angular ngati radius ya njira ya tinthu tating'onoting'ono ndi 10 cm.
Zokambirana
Amadziwika kuti:
Kulemera kwa chinthu (m) = 1 kilogalamu
Ulalo wa bwalo lolimba (r) = 10 cm = 10/100 = 0,1 mamita
Liwiro la angular (ω) = ma radians awiri/sekondi
Anafunsa kuti: Mphamvu ya angular
Yankho:
Fomula ya mphindi ya inertia ya tinthu:
Ine = Mr.² = (1)(0,1)² = (1)(0,01) = 0,01 kg m²

Mphamvu ya angular:
L = I ω = (0,01)(2) = 0,02 kg m²/s

Lamulo losunga mphamvu ya angular

5. Disiki yolimba yozungulira yofanana poyamba imazungulira pa mzere wake ndi liwiro la angular la 5 rad/s. Denga la diski limafanana ndi dera lopingasa. Kulemera ndi utali wa diski ndi 2 kg ndi 0,2 metres. Ngati mphete yokhala ndi kulemera kwa 0,1 kg ndi utali wa mamita 0,2 yayikidwa pamwamba pa diski, pomwe pakati pa mpheteyo pali pamwamba pa pakati pa diski, ndiye kuti diski ndi mpheteyo zidzazungulira pamodzi ndi liwiro la angular la…
Zokambirana
Amadziwika kuti:
Kulemera kwa silinda yolimba (m₁) = 2 kilogalamu
Ulalo wa silinda yolimba (r)₁) = mamita 0,2
Liwiro la angular la silinda yolimba (ω₁) = 5 rad/s
Kulemera kwa mphete (m)₂) = 0,1 kilogalamu
Utali wozungulira wa mphete (r)₂) = mamita 0,2
Anafunsa kuti: Liwiro la masilinda ndi mphete zozungulira
Yankho:
Nthawi ya kulephera kwa silinda yolimba: I = 1⁄2 m₁ r₁² = 1⁄2 (2)(0,2)² = (1)(0,04) = 0,04 kg m²
Nthawi ya inertia ya mphete: Ine = mr² = (0,1)(0,2)² = (0,1)(0,04) = 0,004 kg m²
Nthawi ya kulephera kwa silinda yolimba ndi mphete (I) = 0,04 + 0,004 = 0,044 kg m²

Mphamvu yoyambirira ya angular (L)₁) = Mphamvu yomaliza ya angular (L₂)
I₁ ω₁ = Ine₂ ω₂
(0,04)(5) = (0,044)(ω₂)
(0,2) = (0,044)(ω₂)
ω₂ = 0,2 : 0,044
ω₂ = 4,5 rad/s

6. Wovina ballet amazungulira ndi manja ake atatambasulidwa kutalika kwa 150 cm ndi liwiro la ngodya la ma radian 10 pa sekondi. Kenako wovinayo amapinda manja ake kutalika kwa 75 cm pa chigongono. Kodi liwiro lomaliza la ngodya ndi lotani?
Zokambirana
Amadziwika kuti:
Ulalo wozungulira 1 (r)₁) = 150 cm = 1,5 mamita
Ulalo wozungulira 2 (r)₂) = 75 cm = 0,75 mamita
Liwiro la angular 1 (ω₁) = 10 rad/s
Anafunsa kuti: Liwiro la angular 2 (ω₂)
Yankho:
Nthawi yoyamba ya inertia: I₁ = Bambo.₁² = (m)(1,5)² = 2,25 m
Nthawi yomaliza ya inertia: I₂ = Bambo.₂² = (m)(0,75)² = 0,5625 m

Mphamvu yoyambirira ya angular (L)₁) = Mphamvu yomaliza ya angular (L₂)
I₁ ω₁ = Ine₂ ω₂
(2,25 m)(10) = (0,5625 m)(ω₂)
22,5 m = (0,5625 m)(ω₂)
22,5 = (0,5625)(ω₂)
ω₂ = 22,5/0,5625
ω₂ = 40 rad/s

7. Disiki yolimba yozungulira yofanana imazungulira pa mzere wake ndi liwiro la angular la 4 rad s.^-1Kulemera ndi utali wa diski ndi 1 kg ndi 0,5 m. Ngati mphete yayikidwa pamwamba pa diski yomwe ili ndi utali ndi utali wa 0,2 kg ndi 0,1 m ndipo pakati pa mpheteyo pali pamwamba penipeni pa diski yolimba yozungulira, ndiye kuti diski yolimba yozungulira ndi mpheteyo zidzazungulira limodzi ndi liwiro la angular...
A. 1 rad/s
B. 2 rad/s
C. 3 rad/s
D. 4 rad/s
E. 5 rad/s

Zokambirana :

Nthawi ya Inertia silinda yolimba : I = ½ mr² = ½ (1 kg)(0,5 m)² = (0,5)(0,25) = 0,125 kg m²
Nthawi ya Kusakhazikika kwa mphete: Ine = mr² = (0,2 kg)(0,1 m)² = (0,2)(0,01) = 0,002 kg m²

Mphamvu Yoyamba ya Angular (L)₁) = Mphamvu Yomaliza ya Angular (L)₂)

I₁ ω₁ = Ine₂ 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

Yankho lolondola ndi D.