Saurin kusurwa da saurin layi - matsaloli da mafita

1. Ƙwallo a ƙarshen igiya tana juyawa daidai gwargwado a cikin da'irar kwance ta radius mita 2 a saurin kusurwa mai ɗorewa 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) = mita 0.5 a s, mita 1, mita 3

Gudun kusurwa = 10 radians s / se cond

Ana so: Gudun 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 5 s / se yanayin

(b) Gudun layi (v) na wani wuri da ke r = mita 1

v = r ω = (mita 1)(10 rad/s) = mita 10 s / se yanayin

(c) Saurin layi (v) na wani wuri da ke r = mita 2 a cikin s

v = r ω = (mita 2 s )(10 rad/s) = mita 20 s / se yanayin

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

(a) wani wuri da ke da nisan santimita 5 daga tsakiya

(b) wani wuri da ke da nisan santimita 10 daga tsakiya

An sani:

Radius (r) = 5 cm da 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 tayar mai tsawon santimita 30 a radius, a kusa da da'ira a gudun mita 10/dakika.

Menene girman saurin kusurwa?

An sani:

Radius ( r) = 30 cm = mita 0.3 a s

Saurin layi (v) = mita 10 a minti ɗaya

Ana so: saurin kusurwa

Magani:

ω = v / r = 10 / 0.3 = 33 radians s / se cond

4. Motar da ke da tayoyi masu diamita santimita 50 tana tafiya mita 10 cikin daƙiƙa 1. Menene saurin kusurwa?

An sani:

Radius (r) = mita 0.25

Gudun layi na wani wuri a gefen tayoyin (v) = mita 10 s / se cond

Ana so: Gudun kusurwa

Magani:

ω = v / r = 10 / 0.25 = 40 radians s / se cond

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

An sani:

Radius (r) = 20 cm = mita 0.2 a s

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

Ana so: nesa

Magani:

Gudun gefen tayoyin:

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

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 nisan shine mita 25 a sakan daya.

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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