Su'aalaha tusaalaha ah ee dhaqdhaqaaqa xagasha

7 Tusaalooyin oo ah Dhibaatooyinka Dhaqdhaqaaqa Angular

Dhaqdhaqaaqa Angular

1. Shay ayaa leh daqiiqad firfircoon 2 kg m² oo ku wareego dhidib go'an oo leh xawaaraha xagal 1 rad/s. Immisa? dhaqdhaqaaq xagal ah shaygaas?
Dood
Waa la ogyahay in:
Daqiiqadda firfircoonida (I) = 2 kg m²
Xawaaraha xagasha (ω) = 1 rad/s
La weydiiyay: Xawaaraha xagasha (L)
Jawaab:
Qaacidada dhaqdhaqaaqa xagasha:
L = I ω
Sharaxaad: L = dhaqdhaqaaq xagal (kg m²/ s), I = daqiiqadda firfircoonida (kg m)²), ω = xawaare xagal (rad/s)
Dhaqdhaqaaq xagal:
L = I ω = (2)(1) = 2 kg m²/s

2. Barkinta adag ee saxanka waxay leedahay cufnaan dhan 2 kg iyo gacan 0,1 mitir. Haddii barkintu ay ku wareegto dhidibkeeda iyadoo xawaare xagal joogto ah oo ah 2 rad/ilbiriqsi, waa maxay xawaaraha xagasha ee barkintu?
Dood
Waa la ogyahay in:
Cufka saxanka adag (m) = 2 kiilogaraam
Radius-ka khaanadaha adag (r) = 0.1 mitir
Xawaaraha xagasha (ω) = 2 radiyaan/ilbiriqsi
La weydiiyay: Xawaaraha xagasha ee roogga
Jawaab:
Qaacidada daqiiqadda firfircoonida ee saxanka adag haddii uu ku wareego dhidib sida ka muuqata sawirka:
I = 1/2 mr²
Sharaxaad: I = daqiiqadda firfircoonida (kg m²), m = cuf (kg), r = gacan (mitir)
Daqiiqadda firfircoonida saxanka adag:
I = 1/2 (2)(0,1)² = (1)(0,01) = 0,01 kg m²

Dhaqdhaqaaq xagal:
L = I ω = (0,01)(2) = 0,02 kg m²/s

3. Kubad adag oo miisaankeedu yahay 2 kg iyo gacan 0,2 mitir ayaa ku wareegta dhidibkeeda iyadoo xawaare xagal ah uu yahay 4 rad/s. Go'aami xawaaraha xagasha ee kubbadda adag!
Dood
Waa la ogyahay in:
Cufka kubad adag (m) = 2 kiilo garaam
Gacanka wareegsan adag (r) = 0,2 mitir
Xawaaraha xagasha (ω) = 4 radiyaan/ilbiriqsi
La weydiiyay: Dhaqdhaqaaq xagal ah oo goob adag ah
Jawaab:
Qaacidada daqiiqadda firfircoonida kubbadda adag haddii ay ku wareegto dhidib sida ku cad sawirka:
I = (2/5) mr²
Sharaxaad: I = daqiiqadda firfircoonida (kg m²), m = cuf (kg), r = gacan (mitir)
Daqiiqad firfircoon oo ah goob adag:
I = (2/5)(2)(0,2)² = (4/5)(0,04) = 0,032 kg m²

Dhaqdhaqaaqa xagasha ee goob adag:
L = I ω = (0,032)(4) = 0,128 kg m²/s

4. Shay culeyskiisu yahay 1 kg ayaa ku wareegaya goobaabin leh xawaare xagal oo joogto ah oo ah 2 rad/s. Go'aami xawaaraha xagal haddii gacanka wadada walaxda uu yahay 10 cm.
Dood
Waa la ogyahay in:
Cufka shayga (m) = 1 kiilo garaam
Gacanka wareegsan adag (r) = 10 cm = 10/100 = 0,1 mitir
Xawaaraha xagasha (ω) = 2 radiyaan/ilbiriqsi
La weydiiyay: Xawaaraha xagasha
Jawaab:
Qaacidada daqiiqadda firfircoonida ee walaxda:
Aniga = Mudane² = (1)(0,1)² = (1)(0,01) = 0,01 kg m²

Dhaqdhaqaaq xagal:
L = I ω = (0,01)(2) = 0,02 kg m²/s

Sharciga ilaalinta xawaaraha xagasha

5. Saxan silindaal adag oo isku mid ah ayaa marka hore ku wareegaya dhidibkiisa xawaare xagal ah oo ah 5 rad/s. Saxanka saxanku wuxuu barbar socdaa diyaaradda toosan. Cufnaanta iyo gacanka saxanku waa 2 kg iyo 0,2 mitir. Haddii giraan cufkiisu yahay 0,1 kg iyo gacanka 0,2 mitir la dhigo dusha sare ee saxanka, halkaas oo bartamaha faraantigu uu si toos ah uga sarreeyo bartamaha saxanka, markaas saxanka iyo giraantu way isla wareegi doonaan iyadoo xawaare xagal ah...
Dood
Waa la ogyahay in:
Cufka dhululubo adag (m₁) = 2 kiilo garaam
Radius-ka dhululubo adag (r)₁) = 0,2 mitir
Xawaaraha xagal ee dhululubo adag (ω)₁) = 5 rad/s
Cufka giraanta (m)₂) = 0,1 kiilo garaam
Gacanka giraanta (r)₂) = 0,2 mitir
La weydiiyay: Xawaaraha xagal ee dhululubada iyo faraantiga
Jawaab:
Daqiiqadda firfircoonida dhululubo adag: I = 1⁄2 m₁ r₁² = 1⁄2 (2)(0,2)² = (1)(0,04) = 0,04 kg m²
Daqiiqadda firfircoonida giraanta: I = mr² = (0,1)(0,2)² = (0,1)(0,04) = 0,004 kg m²
Daqiiqadda firfircoonida dhululubo adag iyo giraan (I) = 0,04 + 0,004 = 0,044 kg m²

Dhaqdhaqaaqa xagasha bilowga ah (L)₁) = Dhaqdhaqaaqa xagasha kama dambaysta ah (L₂)
I₁ ω₁ = Aniga₂ 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. Qoob-ka-cayaar ballet ah ayaa wareegaysa iyadoo gacmaheeda u fidsan yihiin dherer dhan 150 cm iyo xawaare xagal ah oo ah 10 radians/ilbiriqsi. Kadibna qoob-ka-cayaaruhu wuxuu gacmaheeda u laabayaa dherer dhan 75 cm xusulka. Waa maxay xawaaraha xagal ee ugu dambeeya?
Dood
Waa la ogyahay in:
Gacanka 1 (r)₁) = 150 cm = 1,5 mitir
Gacanka 2 (r)₂) = 75 cm = 0,75 mitir
Xawaaraha xagasha 1 (ω)₁) = 10 rad/s
La weydiiyay: Xawaaraha xagasha 2 (ω)₂)
Jawaab:
Daqiiqadda hore ee firfircoonida: I₁ = Mudane.₁² = (m)(1,5)² = 2,25 m
Daqiiqaddii ugu dambeysay ee firfircoonida: I₂ = Mudane.₂² = (m)(0,75)² = 0,5625 m

Dhaqdhaqaaqa xagasha bilowga ah (L)₁) = Dhaqdhaqaaqa xagasha kama dambaysta ah (L₂)
I₁ ω₁ = Aniga₂ ω₂
(2,25 m)(10) = (0,5625 m)(ω)₂)
22,5 m = (0,5625 m)(ω)₂)
22,5 = (0,5625)(ω₂)
ω₂ = 22,5/0,5625
ω₂ = 40 rad/s

7. Saxanka qaabaysan ee isku midka ah ayaa marka hore ku wareegaya dhidibkiisa isagoo wata xawaare xagal ah oo ah 4 rad s.^-1Cufnaanta iyo gacanka saxanka waa 1 kg iyo 0,5 m. Haddii giraan la saaro dusha sare ee saxanka oo leh cuf iyo gacanka 0,2 kg iyo 0,1 m oo bartamaha giraanku uu si sax ah uga sarreeyo bartamaha saxanka silsiladda adag, markaa saxanka silsiladda adag iyo giraantu waxay si wadajir ah u wareegi doonaan iyagoo wata xawaare xagal ah...
A. 1 rad/s
B. 2 rad/s
C. 3 rad/s
D. 4 rad/s
E. 5 rad/s

Dood :

Daqiiqadda Inertia dhululubo adag: I = ½ mr² = ½ (1 kg)(0,5 m)² = (0,5)(0,25) = 0,125 kg m²
Daqiiqadda Inertia ee giraanta: I = mr² = (0,2 kg)(0,1 m)² = (0,2)(0,01) = 0,002 kg m²

Mowjadda Angular ee Bilowga ah (L ₁ ) = Mowjadda Angular ee Ugu Dambeysa (L ₂ )

I ₁ ω ₁ = I ₂ ω ₂

(0,125 kg m ² )(4 rad/s) = (0,125 kg m ² + 0,002 kg m ² )(ω ₂ )

(0,5) = (0,127)(ω ₂ )

ω ₂ = 0,5: 0,127

ω ₂ = 4 rad/s

Jawaabta saxda ah waa D.