Physics

9 Ma'aunin zafin jiki mai canzawa (ma'aunin Celsius ma'aunin Fahrenheit ma'aunin Kelvin)

1. 50 ^oC = …… ^oF?

Magani

A yanayin da aka saba gani matsa lamba, wurin daskarewar ruwa shine 0 ^oC a kan Sikelin Celsius kuma 32 ^oF akan ma'aunin Fahrenheit. A matsakaicin matsin lamba na yanayi, wurin tafasar ruwa shine 100 ^oC akan sikelin Celsius da 212 ^oF a ma'aunin Fahrenheit.

0 ^oC=32 ^oF da 100 ^oC=212 ^oF. Canji na 5 C^o = canjin 9 F^o.

Don ma'aunin Celsius, nisan da ke tsakanin 0 ^oC da 100 ^oAn raba C zuwa tazara 100 daidai gwargwado. Ga ma'aunin Fahrenheit, tazara tsakanin 0 ^oC da 100 ^oAn raba C zuwa tazara 180 daidai gwargwado.

T^oF = (180/100) T^oC + 32

T^oF = (9/5) T^oC + 32

T^oF = (9/5) 50 + 32

T^oF = (9) 10 + 32

T^oF=90 + 32

T^oF=122

50 ^oC=122 ^oF

2. 86 ^oF = …… ^oC?

Magani

T^oC = (100/180)(T)^oF – 32)

T^oC = (5/9)(T)^oF – 32)

T^oC = (5/9)(86 – 32)

T^oC = (5/9)(54)

T^oC = (5)(6)

T^oC=30

86 ^oF=30 ^oC

3. 50^oC = ….. K?

Magani

T = T ^oC + 273

T = 50 + 273

T = 323

50 ^oC = ba 323 K

4. 212^oF = ….. K?

Magani

T^oC = (100/180)(T)^oF – 32)

T^oC = (5/9)(T)^oF – 32)

T^oC = (5/9)(212 – 32)

T^oC = (5/9)(180)

T^oC = (5)(20)

T^oC=100

212 ^oF=100 ^oC + 273

212 ^oF=373 K

 

5. x ku ^oC = x ^oF

x = ……?

Magani

1: Canza ma'aunin Celsius zuwa ma'aunin Fahrenheit

2: Canza ma'aunin Fahrenheit zuwa ma'aunin Celsius

6. 122°F = ….. Celsius

Magani

Za a iya rubuta canjin da ke tsakanin ma'aunin zafin jiki guda biyu:

T_C = 5/9 (T)_F - 32)

T_C = Zafin jiki a Celsius, T_F = zafin jiki a Fahrenheit

Zafin Celsius:

T_C = 5/9 (122 – 32) = T_C = 5/9 (90) = 5 (10)

T_C = 50 ^oC

7. Hoton da ke ƙasa yana nuna ma'aunin zafin jiki na a ruwa mai ma'aunin zafi na Fahrenheit! Idan ana auna zafin ruwan ta amfani da ma'aunin zafi na sikelin Celsius, to, abin da ke zafin ruwae.

An sani:

Fahrenheit sikelin (T_F) = 95^oF

Ana so: Sikelin Celsius

Magani:

A matsin lamba na 1 atm, wurin daskarewar ruwa is 0 °C yayin da ma'aunin Fahrenheit shine 32 ^oF. Akasin haka, twurin tafasar ruwa don CElsius sikelin shine 100 ^oC yayin da sikelin Fahrenheit is 212 ^oF.

A ma'aunin Celsius, tsakanin 0 °C da 100 °C akwai 100 ° yayin da a ma'aunin Fahrenheit tsakanin 32 °F zuwa 212 °F akwai 180 °.

T_C = 100/180 (T)_F - 32)

T_C = 5/9 (T)_F - 32)

T_C = 5/9 (95 - 32)

T_C = 5/9 (63)

T_C = 315 / 9

T_C = 35^oC

8. Dangane da hoton da ke ƙasa, ƙayyade tyanayin zafi P akan ma'aunin zafi na Celsius.

Magani

T_C = 100/180 (T)_F - 32)

T_C = 5/9 (T)_F - 32)

T_C = 5/9 (104 – 32)

T_C = 5/9 (72)

T_C = 360 / 9

T_C = 40 ^oC

9. Idan zafin ma'aunin Celsius ya nuna a cikin hoton da ke ƙasa, to a tantance zafin ma'aunin Fahrenheit kamar yadda aka nuna a cikin hoton da ke ƙasa.

Magani:

T^oF = (180/100) T^oC + 32

T^oF = (9/5) T^oC + 32

T^oF = (9/5) 60 + 32

T^oF = (9) 12 + 32

T^oF=108 + 32

T^oF=140

1. Canza ma'aunin zafin jiki
2. Fadada layin layi
3. Faɗaɗa yanki
4. Fadada ƙara
5. Heat
6. Daidaiton zafi na inji
7. Ƙarfin zafi da zafi na musamman
8. Zafin da ke ɓoye, zafin haɗuwa, zafin tururi
9. Ajiye makamashi don canja wurin zafi

Karin bayani

1. Jadawalin ƙarfi (F) idan aka kwatanta da tsawaitawa (x)) da aka nuna a cikin hoton da ke ƙasa. Nemo ma'aunin bazara!

Magani

Dokar Hooke dabara:

ku = F / x

F= karfi (Newton)

k = madaidaitan bazara (Newton/mita)

x = canjin tsayi (mita)

Madaidaicin bazara:

k = 10 / 0.02 = 20 / 0.04

k = 500 N/m

2. Ƙaddara spring m.

Magani

Madaidaicin bazara:

ku = F / x

k = 5 / 0.01 = 10 / 0.02 = 15 / 0.03 = 20 / 0.04

k = 500 N/m

3. Bazara ta A tana da tsayin asali na 60 cm, kuma bazara ta B tana da tsayin asali na 90 cm. Bazara ta A tana da tsayin 100 N/m, bazara ta B kuma tana da tsayin 200 N/m. Rabon canjin tsawon bazara A zuwa canjin tsawon bazara B shine…

An sani:

Daidaiton bazara A (k)_A) = 100 N/m

Daidaiton bazara B (k)_B) = 200 N/m

Ƙarfi a kan bazara A (F)_A) = F

Ƙarfi a kan bazara B (F)_B) = F

SE busca: Δl_A : Δl_B

Magani:

Tsarin dokar Hooke:

Δl = F / k

Δl = canjin tsayi, F = ƙarfi, k = m

Canjin tsawon bazara A:

Δl_A = F_A /k_A = F / 100

Canjin tsawon bazara B:

Δl_B = F_B /k_B = F / 200

Rabon canjin tsawon bazara A zuwa canjin tsawon bazara B:

Δl_A : Δl_B

F/100: F/200

1 / 100: 1 / 200

1 / 1: 1 / 2

2: 1

4. Zaren nailan mai tsayin asali na santimita 20, ana jan shi da ƙarfin N10. Canjin tsawon zaren shine santimita 2. A ƙayyade girman ƙarfin idan canjin tsawon shine santimita 6.

An sani:

Ƙarfi (F) = 10 N

Canjin tsayi (Δl) = 2 cm = 0.02 m

Ana so: girman ƙarfin (F) idan Δl = 0.06 m.

Magani:

Kullum:

k = F / Δl

k = 10 / 0.02 = 500 N/m

Girman ƙarfin (F) idan Δl = 0.06 m:

F = kx

F = (500)(0.06)

F = 30N

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1. Dokar Hooke
2. Damuwa, damuwa, tsarin Young

Karin bayani

Tsarin Matsalar Damuwa ta Matasa - Matsaloli da Magani

1. Zaren nailan yana da diamita na 2 mm, wanda ƙarfin N100 ke ja. Ka ƙayyade damuwa!

An sani:

Force (F) = 100 N

Diamita (d) = 2 mm = 0.002 m

Radius (r) = 1 mm = 0.001 m

Ana so: Danniya

Magani:

Yanki:

A = π r²

A = (3.14)(0.001 m)² = 0.00000314 m²

A = 3.14 x 10^-6 m²

Damuwa:

2. Igiya tana da tsawon asali na santimita 100, ƙarfin da ke jan ta. Canjin tsawon igiyar shine milimita 2. Ka ƙayyade irin ƙarfin!

An sani:

Tsawon asali (l)₀) = 100 cm = 1 m

Canjin tsayi (Δl) = 2 mm = 0.002 m

Ana so: Nau'in

Magani:

A sjirgin ƙasa:

3. Zaren da diamitansa ya kai mm 4 yana da tsayin asali na mita 2. Ana jan zaren da ƙarfin N 200. Idan tsawon bazara na ƙarshe ya kai mita 2.02, a tantance: (a) damuwa (b) damuwa (c) Tsarin Young

An sani:

Diamita (d) = 4 mm = 0.004 m

Radius (r) = 2 mm = 0.002 m

Yanki (A) = π r² = (3.14)(0.002 m)²

Yanki (A) = 0.00001256 m² = 12.56 x10^-6 m²

Ƙarfi (F) = 200 N

Tsawon asali na bazara (l)₀= 2m

Canjin tsayi (Δl) = 2.02 – 2 = 0.02 m

Ana so: (a) Damuwa (b) Damuwa c) Tsarin Young

Magani:

(a) stress

(b) Matsalar

(C) Tsarin matasa

4. Zaren yana da diamita na 1 cm kuma tsawon asali na 2 m. Ana jan zaren da ƙarfin 200 N. Kayyade canjin tsawon zaren! Matakan Young na zaren = 5 x 10⁹ N / m²

An sani:

Tsarin Young (E) = 5 x 10⁹ N / m²

Tsawon asali (l)₀= 2m

Ƙarfi (F) = 200 N

Diamita (d) = 1 cm = 0.01 m

Radius (r) = 0.5 cm = 0.005 m = 5 x 10^-3 m

Yanki (A) = π r² = (3.14)(5 x 10^-3 m)² = (3.14)(25 x 10^-6 m²)

Yanki (A) = 78.5 x 10^-6 m² = 7.85 x10^-5 m²

Nema : Canjin tsayi (Δl)

Magani:

Tsarin tsarin Young:

Canjin tsayi :

5. Siminti yana da tsayin mita 5 kuma yana da faɗin yanki na mita 3³ goyi bayan a taro na kilogiram 30,000. Ƙayyade (a) Damuwa (b) Nauyin (c) Canjin tsayi! Hanzarta saboda nauyi (g) = 10 m/s²Tsarin siminti na Young = 20 x 10⁹ N / m²

An sani:

Tsarin siminti na Young = 20 x 10⁹ N / m²

Tsawon farko (l)₀) = mita 5

Yankin sashi (A) = 3 m²

Weight (w) = mg = (30,000)(10) = N 300,000

Ana so: (a) Damuwa (b) Damuwa (c) Canjin tsayi!

Magani:

(a) Damuwa

(b) Matsalar

(c) Canjin tsayi

1. Dokar Hooke
2. Damuwa, damuwa, tsarin Young

Karin bayani

1. Ana juya ƙwallon, wanda aka haɗa a ƙarshen igiya mai kwance, a cikin da'irar radius 20 cm. Ƙwallon tana kusa da 360^o a kowace daƙiƙa. Ƙayyade girman hanzarin tsakiya!

An sani:

Gudun kusurwa (ω)) = 360^o/daki = juyin juya hali 1/daki = 6.28 radians/daki

Radius (r) = 20 cm = 0.2 m

Ana so: Hanzarin tsakiya (a)_r)

Magani:

a_r = v² /r —> v = r ω

a_r = (r ω)² / r = r² ω² /r

a_r =r ω²

a_s = hanzarin tsakiya, v = saurin layi, r = radius, ω = tururuwa mai daidaituwa

Girman hanzarin centripetal :

a_r =r ω² a_r = (0,2 m)(6.28 rad/s)

a_r = 1.256m/s²

2. Tayar da ke da santimita 30 a radius tana juyawa a gudun 180 rpm. Kayyade hanzarin centripetal na wani wuri a gefen tayar!

An sani:

Radius (r) = 30 cm = 0.3 m

Gudun kusurwa (ω) = Juyi 180 / daƙiƙa 60 = Juyi 3 / daƙiƙa = (3)(Radian 6.28) / daƙiƙa = Radian 18.84/daƙiƙa

Ana so: hanzarin tsakiya (a_r) na r = 0.3 m

Magani:

Girman hanzarin centripetal:

a_r =r ω²

a_r = (0.3 m)(18.84) rad / s)

a_r = 5.65m/s²

3. Motar tsere tana tafiya a kan hanyar zagaye ta radius mita 50. Idan gudun motar ya kai kilomita 72/h, a tantance girman saurin centripetal!

An sani:

Radius (r) = mita 50

Gudun (v) = 72 km/h = (72)(mita 1000) / daƙiƙa 3600 = mita 20/daƙiƙa

Nema : girman hanzarin centripetal (a_r)

Magani:

a_r = v² / r = 20² / 50 = 400 / 50 = 8 m/s²

4. Mota tana da matsakaicin saurin gudu na centripetal na 10 m/s², don motar ta iya juyawa ba tare da ta fice daga hanyar da ke lanƙwasa ba. Idan motar tana tafiya a daidai gudun kilomita 108/h, menene radius na lanƙwasa mara bango?

An sani:

Hanzarin tsakiya (a_r) = 10 m/s²

Gudun mota (v) = 108 km/h = (108)(1000) / 3600 = mita 30s/second

Ana so: radius (r)

Magani:

r = v² / Zuwa_r

r = 30² / 10 = 900 / 10 = mita 90s

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1. Matsalolin da ke tattare da mafita na raka'a kusurwa suna canza yanayinsu
2. Matsalolin da mafita na ƙaura ta kusurwa da kuma matsalolin ƙaura ta layi
3. Samfurin saurin kusurwa da saurin layi tare da mafita
4. Samfurin matsalolin haɓaka kusurwa da haɓaka layi tare da mafita
5. Samfuran matsalolin motsi na zagaye iri ɗaya tare da mafita
6. Samfurin matsalolin hanzarin centripetal tare da mafita
7. Samfuran matsalolin motsin zagaye marasa tsari tare da mafita

Karin bayani

1. Motar hawa uku0 cm a cikin radius yana juyawa akai-akai 5 rad/s²Menene girman hanzarta layi na wani wuri da ke (a) 10 cm daga tsakiya (b) 20 cm daga tsakiya (c) a gefen tayoyin?

An sani:

Radius (r) = 30 cm = 0.3 m

Hanzarin kusurwa (α) = 5 rad/s²

Ana so: hanzarta layi (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m

Magani:

Alaƙa tsakanin hanzarin layi (a) da hanzarin kusurwa:

a = r α

(A) hanzarin layi, r = 0.1 m

a = (0.1 m)(5 rad/s²) = 0.5 m/s²

(B) hanzarin layi, r = 0.2 m

a = (0.2 m)(5 rad/s²) = 1 m/s²

(C) hanzarin layi, r = 0.3 m

a = (0.3 m)(5 rad/s²) = 1.5 m/s²

2. Kuraje mai tsawon santimita 50 a radius. Idan saurin gudu na layi na wani wuri da ke gefen kuraje ya kai mita 2/s², ƙayyade hanzarin kusurwa na pulley!

An sani:

Radius (r) = 50 cm = 0,5 m

hanzarin layi (a) = 2 m/s²

Ana so: hanzarin kusurwa

Magani:

α = a / r = 2 / 0.5 = 4 rad/s²

3. Ruwan wukake a cikin injin niƙa mai tsawon santimita 20 a radius, da farko a lokacin hutawa. Bayan daƙiƙa 2, ruwan wukake suna juyawa 10 rad/s. A ƙayyade girman saurin layi (a) wani wuri da ke da santimita 10 daga tsakiya (b) wani wuri da ke gefen ruwan wukake.

An sani:

Radius (r) = 20 cm = 0.2 m

Saurin kusurwa na farko (ω_o) = 0

Saurin kusurwa na ƙarshe (ω_t) = radian 10/daƙiƙa

Tazarar lokaci (t) = daƙiƙa 2

Ana so: mai saurin gudu na layimizanin wani wuri da ke (a) r = 0.1 m (b) r = 0.2 m

Magani:

ω_t = ω_o + α t

10 = 0 + α (2)

10 = 2 α

α = 10/2

 α = 5 rad/s

(A) hanzarin layi na r = 0.1 m

a = r α = (0.1 m)(5 rad/s²) = 0.5 m/s²

(B) hanzarin layi na r = 0.2 m

a =r α = (0.2 m)(5 rad/s²) = 1 m/s²

4. Ana hanzarta tayoyin 20 cm a radius na tsawon daƙiƙa 2 daga 20 rad/s don hutawa. A ƙayyade girman saurin layi (a) wani wuri da ke da nisan 10 cm daga tsakiya (b) wani wuri da ke da nisan 10 cm daga tsakiya.

An sani:

Radius (r) = 20 cm = 0.2 m

Saurin kusurwa na farko (ω_o) = 20 rad/s

Saurin kusurwa na ƙarshe (ω_t) = 0

Tazarar lokaci (t) = daƙiƙa 2

Ana so: Hanzarin layi (a) r = 0.1 m (b) r = 0.2 m

Magani:

ω_t = ω_o + α t

0 = 20 + α (2)

-20 = 2 α

α = -20 / 2

 α = -10 rad/s

Alamar korau tana nufin saurin kusurwa yana raguwa.

(A) hanzarin layi na r = 0.1 m

 a =r α = (0.1 m)(-10 rad/s²) = -1 m/s²

(B) hanzarin layi na r = 0.2 m

a = r α = (0.2 m)(-10 rad/s²) = -2 m/s²

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1. Matsalolin da ke tattare da mafita na raka'a kusurwa suna canza yanayinsu
2. Matsalolin da mafita na ƙaura ta kusurwa da kuma matsalolin ƙaura ta layi
3. Samfurin saurin kusurwa da saurin layi tare da mafita
4. Samfurin matsalolin haɓaka kusurwa da haɓaka layi tare da mafita
5. Samfuran matsalolin motsi na zagaye iri ɗaya tare da mafita
6. Samfurin matsalolin hanzarin centripetal tare da mafita
7. Samfuran matsalolin motsin zagaye marasa tsari tare da mafita

Karin bayani

1. Kwallo a ƙarshen igiya tana juyawa daidai gwargwado a cikin da'irar kwance ta radius mita 2 a saurin kusurwa mai daidaito 10 rad/s. Ka ƙayyade girman saurin layi na wani wuri da ke:

(a) Mita 0.5 daga tsakiya

(b) Mita 1 daga tsakiya

(c) Mita 2 daga tsakiya

An sani:

radius (r) = 0.5 mitas, mita 1, mita 3

Gudun kusurwa = 10 radianss/seyanayi

Ana so: The saurin layi

Magani:

v = r ω

v= saurin layi,r = radius, ω = saurin kusurwa

(A) Gudun layi (v) na wani wuri da ke r = mita 0.5

v = r ω = (Mita 0.5)s)(10 rad/s) = mita 5s/seyanayi

(B) Gudun layi (V) na wani wuri da ke a r = mita 1

v = r ω = (Mita 1)(Rad 10/s) = mita 10s/seyanayi

(C) Gudun layi (V) na wani wuri da ke a r = mita 2s

v = r ω = (Mita 2)s)(10 rad/s) = mita 20s/seyanayi

2. Ruwan wukake a cikin injin blender suna juyawa a gudun 5000 rpm. Kayyade girman saurin layi:

(A) wani wuri da ke da santimita 5 daga tsakiya

(B) wani wuri da ke da santimita 10 daga tsakiya

An sani:

radius (r) = 5 cm kuma 10 cm

Gudun kusurwa (ω) = 5000 juyin juya hali / s 60karshen = 83.3 juyin juya hali / seyanayi = (83.3)(radian 6.28) / seyanayi = 523.3 radianss / seyanayi

Ana so: Girman saurin layi

Magani:

(A) Girman saurin layi na wani wuri da ke da nisan mita 0.05 daga tsakiya

v = r ω = (0.05 m)(523.3 rad/s) = 26 m/s

(B) Girman saurin layi na wani wuri da ke da nisan mita 0,1 daga tsakiya

v = r ω = (0.1 m)(523.3 rad/s) = 52 m/s

3. Wani wuri a gefen tayoyin 30 cm a cikin radius, a kusa da da'ira a gudun da ba ya canzawa Mita 10/daƙiƙa.

Menene girman saurin kusurwa?

An sani:

Radius (r) = 30 cm = mita 0.3s

Gudun layi (v) = mita 10s/seyanayi

Ana so: saurin kusurwa

Magani:

ω = v / r = 10 / 0.3 = radian 33s/seyanayi

4. Mota mai tayoyi masu diamita santimita 50 tafiyalmita 10 a cikin 1 na biyu. Menene saurin kusurwa?

An sani:

radius (r) = mita 0.25

Saurin layi na a alama a gefen tayar (v) = mita 10s/seyanayi

SE busca: Gudun kusurwa

Magani:

ω = v / r = 10 / 0.25 = radian 40s/seyanayi

5. Gudun kusurwa na tayoyin 20 cm a cikin radians shine 120 rpm. Menene distance idan motar ta yi tafiya cikin daƙiƙa 10.

An sani:

radius (r) = 20 cm = mita 0.2s

Gudun kusurwa = 120 sakewa / 60 secyanayi = 2 sakewa / seyanayi = (2)(6.28) radians / seyanayi = 12.56 radianss / seyanayi

Ana so: distance

Magani:

gudu gefen tayoyin:

v = r ω = (mita 0.2)s)(12.56 radians/seyanayi) = mita 2.5s/seyanayi

2.5 mitas / second yana nufin wani wuri a gefen tafiyar tayoyin 2.5 mitas kowane daƙiƙa 1. bayan 10 gayanayi, ma'anar tana tafiya 25 mitas.

Don haka nisa shine 25 mitas.

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1. Matsalolin da ke tattare da mafita na raka'a kusurwa suna canza yanayinsu
2. Matsalolin da mafita na ƙaura ta kusurwa da kuma matsalolin ƙaura ta layi
3. Samfurin saurin kusurwa da saurin layi tare da mafita
4. Samfurin matsalolin haɓaka kusurwa da haɓaka layi tare da mafita
5. Samfuran matsalolin motsi na zagaye iri ɗaya tare da mafita
6. Samfurin matsalolin hanzarin centripetal tare da mafita
7. Samfuran matsalolin motsin zagaye marasa tsari tare da mafita

Karin bayani

Canza raka'o'in kusurwa (digiri, radian, juyin juya hali)

1. ¼ sakewa = ….. ^o (digiri)?

Magani

1 sakewa = 360^o

½ sakewa = 180^o

¼ sakewa = 90^o

2. ½ sakewa = …….. rad ?

Magani

1 sakewa = 2π rad = 2(3.14) rad = 6.28 rad

½ sakewa = pi rad = 3.14 rad

3. 180^o = ….. Rev?

Magani

360^o = 1 sakewa

180^o = ½ sakewa

4. 90^o = ….. radar?

Magani

360^o = 2π rad = 2(3.14) rad = 6.28d

180^o = π rad = 3.14 rad

90^o = ½ π rad = ½ (3.14) = 1.57

5. 60 rad = ….. sakewa ?

Magani

6.28 rad = 1 sakewa

60 rad/6.28 = 9.55 sakewa

6. 40 rad= ….. ^o ?

Magani

6.28 rad = 360^o

40 rad/6.28 = (6.37)(360)^o) = 2292.99^o

Matsar da kusurwa da kuma ƙaura ta layi

1. Tayar keke mai diamita santimita 60 tana juyawa radians 10. Menene matsar layi na wani wuri a gefen tayoyin?

An sani:

Radius (r) = 30 cm = 0.3 m

Kusur (θ)) = 10 radians

Ana so: matsar layi (l)

Magani:

l = r θ

l = (0.3 m)(10 rad)

l = mita 3

2. Tayar mai tsawon santimita 50 a radius tana juyawa 360^oMenene ma'aunin layi na wani wuri a gefen tayoyin?

An sani:

Radius (r) = 50 cm = mita 0.5

Kusurwa (θ) = 360^o = 6.28 radians

Ana so: matsar layi (l)

Magani:

l = r θ

l = (0.5 m)(6.28 rad)

l = mita 3.14

3. Tayar da ke da santimita 50 a radius tana juyawa sau biyu. Menene canjin layi na wani wuri a gefen tayar?

An sani:

Radius (r) = 50 cm = 0,5 m

Kusurwa (θ) = Juyi 2 = (2)(radian 6.28) = radian 12.56

Ana so: ƙaura ta layi (l)?

Magani:

l = r θ

l = (0.5 m)(12.56 rad)

l = 6.28 m

4. Wani wuri a gefen tayoyi mai tsawon mita 2 a radius, yana motsawa mita 100. Ka tantance matsar kusurwa.

An sani:

Radius (r) = ½ (diamita) = ½ (mita 2) = mita 1

Matsar da layi (l) = mita 100

Magani:

(a) Matsar da kusurwa (a cikin radians)

θ = s / r = 100 / 1 = 100 radians

(b) Matsar da kusurwa (a digiri)

1 radians = 360^o

Radians 100 = 100(360)^o) = 36,000 radians

(c) Matsar da kusurwa (a juyin juya hali)

6.28 radians = juyin juya hali 1

Juyin juya hali 36,000 / 6.28 = juyin juya hali 5732,484

5. Ƙwayar cuta tana zagaye da'ira mita 10 kuma tana juyawa 180^oMenene radius ɗin?

An sani:

Matsar da layi (l) = mita 10

Kusurwa (θ) = 180^o = 3.14 radians

Ana so: radius (r)

Magani:

r = lita / θ = 10 / 3.14 = mita 3.18

1. Matsalolin da ke tattare da mafita na raka'a kusurwa suna canza yanayinsu
2. Matsalolin da mafita na ƙaura ta kusurwa da kuma matsalolin ƙaura ta layi
3. Samfurin saurin kusurwa da saurin layi tare da mafita
4. Samfurin matsalolin haɓaka kusurwa da haɓaka layi tare da mafita
5. Samfuran matsalolin motsi na zagaye iri ɗaya tare da mafita
6. Samfurin matsalolin hanzarin centripetal tare da mafita
7. Samfuran matsalolin motsin zagaye marasa tsari tare da mafita

Karin bayani

1. Tayar mita 1 a radius tana hanzarta daidai gwargwado a 2 rad/s²Ƙayyade hanzarin kusurwa da saurin kusurwa na tayoyin, bayan daƙiƙa 2.

An sani:

Radius (r) = mita 1

Hanzarin kusurwa (α)) = 2 rad/s²

SE busca: hanzarta kusurwa da saurin kusurwa bayan daƙiƙa 2.

Magani:

(A) Hanzar kusurwa cikin daƙiƙa 2

Haɓaka kusurwa yana dawwama, don haka bayan daƙiƙa 2, haɓaka kusurwar ƙafafun shine 2 rad/s².

(B) Saurin kusurwa cikin daƙiƙa 2

Hanzarin kusurwa 2 rad/s² yana nufin saurin kusurwa yana ƙaruwa da radians 2/daki a kowace dakika 1. Bayan dakika 1, saurin kusurwa = radians 2/dakika. Bayan dakika 2, saurin kusurwa = radians 4/dakika.

2. Ƙwayar cuta tana hanzartawa daidai gwargwado daga hutawa zuwa rpm 60 cikin daƙiƙa 10. Kayyade girman hanzarin kusurwa!

An sani:

Saurin kusurwa na farko (ω)_o) = 0

Saurin kusurwa na ƙarshe (ω_t) = 60 rpm = juyin juya hali 60 / daƙiƙa 60 = juyin juya hali 1 / daƙiƙa = 6,28 radians/daƙiƙa

Tazarar lokaci (t) = daƙiƙa 10

Ana so: Hanzarin kusurwa (α)

Magani:

ω_o = saurin kusurwa na farko, ω_t = saurin kusurwa na ƙarshe, α = hanzarin kusurwa, t = tazara tsakanin lokaci, θ = kusurwa.

ω_t = ω_o + α t

6.28 = 0 + α (10)

= 6.28 10 α

α = 6.28/10

α = 0.628 rad/s²

Girman hanzarin kusurwa = 0.628 rad/s²

3. Abu yana raguwa daga 20 rad/s zuwa 10 rad/s cikin daƙiƙa 4. Kayyade girman hanzarin kusurwa!

An sani:

Tazarar lokaci (t) = daƙiƙa 4

Saurin kusurwa na farko (ω_o ) = 20 rad/s

Saurin kusurwa na ƙarshe (ω_t) = 10 rad/s

Nema : girman hanzarin kusurwa (α)

Magani:

ω_t = ω_o + α t

10 = 20 + α (4)

10 - 20 = 4 α

-10=4 α

α = -10 / 4

α = – 2.5 rad/s²

Girman hanzarin kusurwa shine -2.5 rad/s²Alamar korau tana nufin abu yana raguwa. Hawan sauri = saurin kusurwa yana ƙaruwa, raguwa = saurin kusurwa yana raguwa.

4. Ana hanzarta abu na tsawon daƙiƙa 2 daga 10 rad/s zuwa 2 rad/s²Kayyade kusurwar da aka zagaye ta hanyar abin!

An sani:

saurin kusurwa na farko (ω_o ) = 10 rad/s

hanzarin kusurwa (α)) = 2 rad/s²

tazara ta lokaci (t) = daƙiƙa 2

Ana so: kusurwa (θ)

Magani:

θ = ku ω_o + ½ α t²

θ = (10)(2) + ½ (2)(2)²)

θ = 20 + (1)(4) = 20 + 4

θ = 24 radians

5. Tayar mota tana raguwa daga 20 rad/s zuwa hutawa bayan zagaye na 20 radians. Kayyade girman saurin kusurwa na tayar!

An sani:

saurin kusurwa na farko (ω_o) = 20 rad/s

gudun kusurwa na ƙarshe (ω_t) = 0

Kusurwa (θ) = 20 radians

Ana so: girman hanzarin kusurwa (α))

Magani:

ω_t² = ω_o² + 2 α θ

= 0 20² + 2 α (20)

0 = 400 + 40 α

400 = – 40 α

α = – 400 / 40

α = – 10 rad/s²

6. Sanda mai tsawon santimita 60 tana juyawa a kusa da maki Q a matsayin axis na juyawa da kuma PQ a matsayin radius na da'ira. Sanda mai saurin PQ daga hutawa zuwa 0.3 rad/s²Menene saurin layi na maki P a t = daƙiƙa 10, idan matsayin kusurwa na farko shine 0.

An sani:

Tsawon sandar PQ = radius na da'ira (r) = 60 cm = 60/100 m = 0.60 m

Saurin kusurwa na farko (ω)_o) = 0 rad/s

Haɓaka kusurwa (α) = 0.3 rad s^-2

Matsayin kusurwa na farko (θ)_o) = 0

Ana so: Gudun layi (v) na maki P a t = daƙiƙa 10

Magani:

Saurin kusurwa na ƙarshe bayan daƙiƙa 10:

ω_t = ω_o + α t = 0 rad/s + (0.3 rad s^-2)(10 s) = 3 rad/s

Saurin layi na ƙarshe bayan daƙiƙa 10:

v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s

7. Abu yana juyawa da saurin farko na 4 rad/s kuma saurin kusurwa shine 0.5 rad/s²Menene saurin abu bayan daƙiƙa 4.

An sani:

Saurin kusurwa na farko (ω)_o) = 4 rad/s

Hanzarin kusurwa (α) = 0.5 rad/s²

Tazarar lokaci (t) = daƙiƙa 4

Ana so: Saurin abu bayan daƙiƙa 4 (ω_t)

Magani:

ω_t = ω_o + α t

ω_t = 4 + (0.5)(4)

ω_t = 4 + 2

ω_t = 6 rad/s

8. A Agogon bango mai diamita na cm 10 yana da allurai uku, kowannensu don nuna awanni, mintuna da daƙiƙa. Kwatanta adadin zagaye na allurar sa'a: allurar minti: allurar ta biyu.

A. 1: 3: 180

B. 1: 12: 720

C. 4: 12: 180

D. 4: 12: 720

An sani:

Awa 1 = mintuna 60

Awa 12 = (12)(minti 60) = mintuna 720

Gudun kusurwa na awa na allura = juyin juya hali 1 / awanni 12 = juyin juya hali 1 / mintuna 720

Gudun kusurwa na mintuna allura = juyin juya hali 1 / awa 1 = juyin juya hali 1 / minti 60

Saurin kusurwa na allura ta biyu = juyin juya hali 1 / minti 1

SE busca: Kwatanta adadin zagaye na allurar sa'a: allurar minti: allurar ta biyu

Magani:

Daidaiton motsi na zagaye:

Gudun kusurwa = adadin juyin juya hali / tazara lokaci

Adadin juyin juya hali = saurin kusurwa x tazara lokaci

A cikin tazara lokaci ɗaya, misali, minti 1, sau nawa juyawar allurar awa, allurar minti, da allurar ta biyu.

Adadin juyawar allurar sa'a = saurin kusurwa x tazara ta lokaci = (juyi 1 / mintuna 720)(minti 1) = juyawa 1/720

Adadin juyawar allurar minti = saurin kusurwa x tazara lokaci = (juyi 1 / mintuna 60)(minti 1) = juyawa 1/60

Adadin juyawar allura ta biyu = saurin kusurwa x tazara ta lokaci = (juyi 1 / minti 1)(minti 1) = 1/1 juyawa

Kwatanta juyin juya hali da dama:

Adadin juyin juya halin allurar sa'a: adadin juyin juya halin allurar minti: adadin juyin juya halin allurar ta biyu.

1/720: 1/60: 1/1

1/720: 12/720: 720/720

1: 12: 720

Amsar da ta dace ita ce B.

9. Kwallo da aka ɗaure da igiya. Ana juya ƙwallon ta yadda za ta motsa a cikin jirgin sama mai zagaye daidai da saman duniya. A cikin wannan motsi, ƙwallon yana ƙaruwa saboda…..

A. Yarjejeniya na iska

B. Weight na ƙwallo

C. Ƙarfin tashin hankali

D. Ƙarfin nauyi

Magani:

Dokar motsi ta biyu ta Newton yana bayyana cewa abu yana hanzarta sauri idan akwai ƙarfin da ya biyo baya. Ana haɗa ƙwallon da igiyar kuma lokacin da igiyar ta juya, ƙwallon ma tana juyawa. Lokacin da ƙwallon ta juya (ƙwallon yana motsawa a cikin da'ira), ƙwallon tana yin saurin centripetal. Duk abubuwan da ke motsawa suna hanzarta centripetal ne. Hanzarin tsakiya yana haifar da centripetal karfiƘarfin centripetal na wannan shari'ar shine ƙarfin tashin hankali.

Madaidaicin amsar ita ce C.

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1. Matsalolin da ke tattare da mafita na raka'a kusurwa suna canza yanayinsu
2. Matsalolin da mafita na ƙaura ta kusurwa da kuma matsalolin ƙaura ta layi
3. Samfurin saurin kusurwa da saurin layi tare da mafita
4. Samfurin matsalolin haɓaka kusurwa da haɓaka layi tare da mafita
5. Samfuran matsalolin motsi na zagaye iri ɗaya tare da mafita
6. Samfurin matsalolin hanzarin centripetal tare da mafita
7. Samfuran matsalolin motsin zagaye marasa tsari tare da mafita

Karin bayani

1. Abu yana motsawa a cikin da'ira tare da saurin kusurwa na 10 rad/s. Ƙayyade (a) Gudun kusurwa bayan daƙiƙa 10 (b) Matsar da kusurwa bayan daƙiƙa 10.

An sani:

Gudun kusurwa (ω) = 10 rad/s

Ana so:

(a) Saurin kusurwa (ω) bayan daƙiƙa 10.

(b) Kusurwa (θ) bayan daƙiƙa 10

Magani:

(A) Saurin kusurwa (ω) bayan daƙiƙa 10

Abu a ciki motsi na zagaye iri ɗaya don haka saurin kusurwa ya kasance daidai, 10 rad/s.

(b) Matsar da kusurwa (θ)

Gudun kusurwa mai daidaito 10 radians/daƙiƙa yana nufin abu mai kusan radians 10 a kowace daƙiƙa. Bayan daƙiƙa 10, abu mai kusan radians 10 x 10 = radians 100.

2. Ƙwayar cuta tana motsawa a cikin da'ira mai saurin mita 10/s. Radius na da'ira = mita 1. Ƙayyade (a) Gudun ƙwayar cuta bayan daƙiƙa 5 (b) Ƙwayar cuta sauyawa bayan daƙiƙa 5 (c) Hanzarin tsakiya.

An sani:

Radius na da'ira (r) = mita 1

Gudun barbashi (v) = 10 m/s

Magani:

(A) Saurin barbashi bayan daƙiƙa 5

Motsin abin yana cikin motsi mai zagaye iri ɗaya don haka gudun ya kasance mai daidaito, 10 m/s.

(B) Fitar da ƙwayoyin cuta bayan daƙiƙa 5

Mita 10/daƙiƙa yana nufin kowace daƙiƙa 1, ƙaurar ƙwayar cuta = mita 10. Bayan daƙiƙa 5, ƙaurar ƙwayar cuta = mita 5 x 10 = mita 50.

(C) Hanzarin tsakiya (a)_r)

a_r = v² / r = 10² / 1 = 100 / 1 = 100 m/s²

3. An juya ƙwallon da aka makala a ƙarshen igiya a cikin da'ira mai radius na mita 2 a gudun da ba ya canzawa na rpm 60. A ƙayyade (a) girman saurin kusurwa bayan daƙiƙa 2 (b) canjin kusurwa bayan minti 1.

An sani:

Radius na da'ira (r) = mita 2

Gudun kusurwa (ω) = 60 rpm = juyin juya hali 60 / minti 1

= Juyi 60 / daƙiƙa 60 = Juyi 1 / daƙiƙa = 2π radians / daƙiƙa

= 2(3.14) radians / daƙiƙa = 6.28 radians / daƙiƙa

Magani:

(A) Saurin kusurwa (ω) bayan daƙiƙa 2

Gudun kusurwar yana da daidaito don haka bayan daƙiƙa 2, saurin kusurwar (ω) = 6.28 radians / daƙiƙa

(B) Matsar da kusurwa (θ)

Saurin kusurwa = juyin juya hali 1/daƙiƙa yana nufin kowace daƙiƙa 1, ƙwallon tana fuskantar juyin juya hali 1. Bayan daƙiƙa 60, ƙwallon tana motsa juyin juya hali 60.

Gudun kusurwa = radians 6.28/daki yana nufin kowace dakika 1, ƙwallon yana motsawa da kusurwar radians 6.28. Bayan dakika 60, ƙwallon yana motsawa radians 376.8.

4. Tayar keke tana juyawa sau 120 cikin daƙiƙa 60. Menene saurin kusurwa?

Magani:

(a) juyin juya hali a minti daya (rpm)

Juyin juya hali 120 / daƙiƙa 60 = juyi 120 / minti 1 = juyi 120 / minti = 120 rpm

(B) digiri a kowace daƙiƙa (^o/ s)

Juyin juya hali 1 = 360^o, Juyin juya hali 120 = 43200^o

Juyawa 120 / daƙiƙa 60 = (120)(360)^o) / daƙiƙa 60 = 43200^o / Daƙiƙa 60 = 720^o/na biyu

(C) radians a kowace daƙiƙa (rad/s)

Juyin juya hali 1 = 6.28 radians

Juyawa 120 / daƙiƙa 60 = (120)(6.28) radians / daƙiƙa 60 = 753.6 radians / daƙiƙa 60 = 12.56 radians/daƙiƙa.

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1. Matsalolin da ke tattare da mafita na raka'a kusurwa suna canza yanayinsu
2. Matsalolin da mafita na ƙaura ta kusurwa da kuma matsalolin ƙaura ta layi
3. Samfurin saurin kusurwa da saurin layi tare da mafita
4. Samfurin matsalolin haɓaka kusurwa da haɓaka layi tare da mafita
5. Samfuran matsalolin motsi na zagaye iri ɗaya tare da mafita
6. Samfurin matsalolin hanzarin centripetal tare da mafita
7. Samfuran matsalolin motsin zagaye marasa tsari tare da mafita

Karin bayani

1. A 0.1ƙwallon -kg, wanda aka haɗa a ƙarshen igiyar kwance, an juya shi a cikin da'irar radius 50 cm da kuma ball saurin kusurwa is Rad guda 4^-1Menene girman centripetal ɗin karfi?

An sani:

Mass (m) = gram 100 = 100/1000 kg = 1/10 kg = 0.1 kg

Gudun kusurwa (ω) = 4 radians/sq.yanayi

Radius (r) = 50 cm = 50/100 m = 0.5 m

Ana so: Ƙarfin tsakiya

Magani:

Ƙarfin centripetal shine ƙarfin da ke samar da ƙarfi ta hanyar yanar gizo hanzarin tsakiya :

ΣF = ma_r

ΣF = mv²/r = m ω² r

ΣF= ƙarfin net = ƙarfin centripetal, m = taro, v = gudun, ω = saurin kusurwa, r = radius

ΣF = m ω² r = (0.1)(4)² (0.5) = (0.1)(16)(0,5) = 0.8 Newtons

2. Kwallo tana juyawa daidai gwargwado a cikin da'irar kwance. Idan saurin ya canza zuwa sau huɗu na ƙimar farko, menene girman ƙarfin centripetal…..

An sani:

Mass = m

Speed = v

Saurin farko = v_o

Radius (r) =r

SE busca: Girman ƙarfin centripetal

Magani:

3. An ƙera lanƙwasa mai kusurwa huɗu na radius R ta yadda mota za ta yi tafiya a gudun 12 ms^-1 zai iya yin shawarwari kan juyawa cikin aminci. gogayya mara motsi tsakanin mota da hanya = 0.4. Menene radius R. Hanzarta saboda nauyi (g) = 10 ms^-2.

An sani:

Speed (v) = 12 m/s

Coefficient na gogayya mai motsi (μ_s) = 0.4

Hanzarta saboda nauyi (g) = 10 m/s²

SE busca: Radius (R)

Magani:

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1. Nauyi da nauyi
2. ƙarfin al'ada
3. Dokar motsi ta biyu ta Newton
4. Ƙarfin gogayya
5. Motsi a kan saman kwance ba tare da ƙarfin gogayya ba
6. Motsin gawawwaki biyu tare da hanzari iri ɗaya a kan saman kwance mai tsauri tare da ƙarfin gogayya
7. Motsi a kan jirgin sama mai karkata ba tare da ƙarfin gogayya ba
8. Motsi a kan jirgin sama mai karkata da ƙarfin gogayya
9. Motsi a cikin lif
10. Motsin jikin mutum yana da alaƙa da igiyoyi da kuma ƙwallo
11. Jikuna biyu masu girman gudu iri ɗaya
12. Zagaye lanƙwasa mai faɗi - yanayin motsi na zagaye
13. Zagaye lanƙwasa mai banked - yanayin motsi na zagaye
14. Motsi iri ɗaya a cikin da'irar kwance
15. Ƙarfin tsakiya a cikin motsi na zagaye iri ɗaya

Karin bayani