Su'aalaha iyo Doodaha Dhaqdhaqaaqa Wareega
Dhaqdhaqaaqa wareegga waa mowduuc muhiim ah oo ku jira fiisigiska, kaasoo ka hadlaya dhaqdhaqaaqa walxaha wareegaya. Dhacdadani waxay ka kooban tahay fikrado badan, sida daqiiqadda inertia, wareegga, sharciga labaad ee wareegga Newton, tamarta dhaqdhaqaaqa wareegga, iyo waxyaabo kaloo badan. Maqaalkani wuxuu soo bandhigi doonaa dhowr dhibaato iyo doodo ku saabsan dhaqdhaqaaqa wareegga si loo caddeeyo fahamkeenna ku saabsan fikradahan.
1. Daqiiqadda Inertia iyo Torque
Su'aal:
Giraan khafiif ah oo miisaankeedu yahay \(2\) kg iyo gacanka \(0.5\) m ayaa ku wareegaysa dhidibka dhexe. Xisaabi daqiiqadda inertia ee giraanta, haddiina la mariyo xoog dhan \(6\) Nm, waa maxay dardargelinta xagasha ka dhalatay?
Dood:
Daqiiqadda inertia \(I\) ee giraanta khafiifka ah ee ku wareegsan dhidibka dhexe waa:
\[ I = MR^2 \]
Iyada oo leh \(M = 2\) kg iyo \(R = 0.5\) m, markaa:
\[ I = 2 \ jeer (0.5)^2 \]
\[ I = 2 \ jeer 0.25 \]
\[ I = 0.5 \, \qoraalka{kg} \, \qoraalka{m}^2 \]
Dardargelinta xagasha (\(\alpha\)) waxaa lagu xisaabin karaa iyadoo la adeegsanayo wareegga (\(\tau\)) iyo daqiiqadda inertia (\(I\)):
\[ \tau = I \alpha \]
\[ \alpha = \frac{\tau}{I} \]
Iyadoo \(\tau = 6\) Nm iyo \(I = 0.5\) kg m²:
\[ \alpha = \frac{6}{0.5} \]
\[ \alpha = 12 \, \qoraalka{rad/s}^2 \]
Markaa, daqiiqadda firfircoonida giraanta waa \(0.5\) kg m² iyo dardargelinta xagasha ka dhalata waa \(12\) rad/s².
2. Tamarta Kinetic-ga Wareega
Su'aal:
Dhululubo adag oo miisaankiisu yahay \(4\) kg iyo gacanka \(0.3\) m ayaa wareegaya iyadoo xawaare xagal ah oo ah \(10\) rad/s. Xisaabi tamarta dhaqdhaqaaqa wareega ee dhululubada.
Dood:
Tamarta dhaqdhaqaaqa wareega (\(K\)) waxaa loo qaabeeyey sidan:
\[ K = \frac{1}{2} I \omega^2 \]
Halkee \(\omega\) uu yahay xawaaraha xagasha, iyo \(I\) uu yahay daqiiqadda inertia. Dhululubo adag (\(I = \frac{1}{2}MR^2\)):
\[ I = \frac{1}{2} \jeer 4 \jeer (0.3)^2 \]
\[ I = 2 \ jeer 0.09 \]
\[ I = 0.18 \, \qoraalka{kg} \, \qoraalka{m}^2 \]
Qiimaha \(I\) iyo \(\omega\) ku beddel isle'egta tamarta wareegga wareegga:
\[ K = \frac{1}{2} \jeer 0.18 \jeer (10)^2 \]
\[ K = 0.09 \jeer 100 \]
\[ K = 9 \, \qoraal{J} \]
Markaa, tamarta dhaqdhaqaaqa wareega ee dhululubada adag waa Joules.
3. Sharciga Labaad ee Wareegga ee Newton
Su'aal:
Giraangiraha jiidista waxay leeyihiin gacan ah oo ah \(0.4\) m iyo daqiiqad ah oo ah \(0.8\) kg m². Xoog \(F\) oo ah \(20\) N ayaa si tangically loogu dhejiyaa geeska giraangiraha. Xisaabi dardargelinta xagasha giraangiraha.
Dood:
Marka hore, waxaan xisaabineynaa xoogga \(\tau\):
\[ \tau = F \times R \]
\[ \tau = 20 \ jeer 0.4 \]
\[ \tau = 8 \, \qoraalka{Nm} \]
Kadib isticmaal sharciga labaad ee Newton si aad u rogto:
\[ \tau = I \alpha \]
\[ \alpha = \frac{\tau}{I} \]
Iyadoo la adeegsanayo \(\tau = 8 \, \text{Nm}\) iyo \(I = 0.8 \, \text{kg m}^2\):
\[ \alpha = \frac{8}{0.8} \]
\[ \alpha = 10 \, \qoraalka{rad/s}^2 \]
Markaa, xawaaraha xagasha ee giraangiraha waa \(10\) rad/s².
4. Xiriirka ka dhexeeya Tangent iyo Turjumaadda
Su'aal:
Kubad miisaankeedu yahay \(1\) kg iyo gacanka \(0.2\) m ayaa rogmanaysa iyada oo aan dhulka ku simbirixanayn xawaare xagal ah oo ah \(5\) rad/s. Xisaabi xawaaraha toosan ee bartamaha cufka kubadda.
Dood:
Xiriirka ka dhexeeya xawaaraha xagal-geeska (\(\omega\)) iyo xawaaraha toosan (\(v\)) ee dhaqdhaqaaqa rogrogidda iyada oo aan simbiriirixanayn waa:
\[ v = \omega R \]
Iyadoo \(\omega = 5\) rad/s iyo \(R = 0.2\) m:
\[ v = 5 jeer 0.2 \]
\[ v = 1 \, \qoraalka{m/s} \]
Markaa, xawaaraha toosan ee bartamaha cufka kubbadda waa \(1\) m/s.
5. Isku-darka Tamarta Kinetic-ga Turjumaadda iyo Wareegga
Su'aal:
Dhululubo adag oo miisaankiisu yahay \(2\) kg iyo gacanka \(0.1\) m ayaa hoos u dhacaya meel u janjeerta dhererkeedu yahay \(3\) m. Xisaabi xawaaraha dhululubada marka uu gaaro salka diyaaradda u janjeerta.
Dood:
Marka dhululubadu rogmato iyada oo aan simbirixan, tamarta awoodda cufisjiidadka waxaa loo beddelaa tamar tarjumaad iyo tamar wareeg ah. Tamarta guud \(E\) waxaa lagu tilmaami karaa sidan:
\[ E = mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 \]
Marka la eego \(I\) dhululubo adag = \(\frac{1}{2}MR^2\), iyo \(\omega = \frac{v}{R}\), isla'egtu waxay noqonaysaa:
\[ mgh = \frac{1}{2}mv^2 + \frac{1}{2}\left(\frac{1}{2}MR^2\right)\left(\frac{v^2}{R^2}\right) \]
\[ 2 \jeer 9.8 \jeer 3 = \frac{1}{2} \jeer 2 \jeer v^2 + \frac{1}{2} \left( \frac{1}{2} \jeer 2 \jeer v^2 \right) \]
\[ 58.8 = v^2 + \frac{1}{2}v^2 \]
\[ 58.8 = \frac{3}{2}v^2 \]
\[ v^2 = \frac{58.8 \times 2}{3} \]
\[ v^2 = 39.2 \]
\[ v = \sqrt{39.2} \]
\[ v \qiyaastii 6.26 \, \qoraalka{m/s} \]
Markaa, xawaaraha dhululubada marka uu gaaro salka diyaaradda u janjeerta waa qiyaastii \(6.26\) m/s.
Gabagabo
Dhibaatooyinkan awgood, waxaan sahaminay dhowr fikradood oo muhiim ah oo ku saabsan dhaqdhaqaaqa wareegga, oo ay ku jiraan daqiiqadda inertia, wareegga, tamarta dhaqdhaqaaqa wareegga, sharciga labaad ee wareegga Newton, iyo xiriirka ka dhexeeya dhaqdhaqaaqa wareegga iyo tarjumaadda. Faham wanaagsan oo ku saabsan fikradahan ayaa naga caawin doona inaan falanqeyno oo aan xallino dhibaatooyinka dhabta ah ee ku lug leh dhaqdhaqaaqa wareegga.
