Tsarin motsin juyawa - matsaloli da mafita

1. Pulley mai lokacin inertia I = 2/5 MR ² yana da nauyin kilogiram 2. Idan lokacin ƙarfi akan pulley shine 4 Nm to menene saurin layi na pulley. Saurin nauyi saboda nauyi shine g = 10 ms ^-2.

An sani : Tsarin motsin juyawa - matsaloli da mafita 1

Lokacin inertia na pulley (I) = 2/5 MR ²

Nauyin kura (M) = 2 kg

Lokacin ƙarfi (τ) = 4 Nm

Saurin gudu saboda nauyi (g) = 10 ms ^-2

Radius na kura (R) = 20 cm = 0.2 m

Ana so: Haɓaka layi (a)

Magani:

Lokacin inertia na pulley (I):

I = 2/5 MR ² = 2/5 (2)(0.2) ² = 2/5 (2)(0.04) = 2/5 (0.08) = 0.16 / 5 = 0.032 kg m ²

Saurin kusurwa (α):

τ = ina

α = τ/I = 4 / 0.032 = 125 rad.s ^-2

Haɓaka layi (a):

a = R α = (0.2)(125) = 25 ms ^-2

Hawan layi na gefen pulley shine 25 ms ^-2.

2. Saurin bugun shine 2 ms ^-2 . Saurin nauyi saboda nauyi shine g = 10 ms ^-2 . Menene lokacin rashin ƙarfin bugun.

An sani:

Haɓakar layi na gefen kura (a) = 2 ms^-2

Saurin gudu saboda nauyi (g) = 10 ms ^-2

Radius na kura (R) = 10 cm = 0.1 m

Nauyin abu (w) = mg = (4)(10) = 40 N

Ana so: Lokacin inertia na pulley

Magani:

Lokacin ƙarfi (τ):

τ = FR = w R = (40) (0.1) = 4 nm

Saurin kusurwa na pulley (α):

a = Rα

α = a/R = 2 / 0.1 = 20 radi.s ^-2

Lokacin inertia na kura (I):

τ = ina

I = τ/α = 4/20 = 0.2 kg m ²

3. Pulley ɗin ya yi sauri a 1 ms ^-2 . Idan radius na pulley ɗin ya kai cm 10, menene lokacin inertia na pulley ɗin.

An sani:

Haɓakar layi na gefen kura (a) = 1 ms^-2

Saurin gudu saboda nauyi (g) = 10 ms ^-2

Radius na kura (R) = 10 cm = 0.1 m

Ƙarfi (F) = 4 N

Ana so: Lokacin inertia na pulley

Magani:

Lokacin ƙarfi (τ):

τ = FR = (4)(0.1) = 0.4 Nm

Haɓaka kusurwar pulley (α):

a = Rα

α = a/R = 1 / 0.1 = 10 radi.s ^-2

Lokacin inertia na pulley (I):

τ = ina

I = τ/α = 0.4/10 = 0.04 kg m ²

Menene daidai da juyawar nauyi a cikin motsi na layi?
- amsa: Daidaiton juyawa na taro a cikin motsi na layi shine lokacin inertia, wanda galibi ana nuna shi azaman $I$ .
Ta yaya karfin juyi yake da alaƙa da motsin juyawa, kuma ta yaya yake kwatantawa da ƙarfi a cikin motsi na layi?
- amsa: Juyin juyi daidai yake da ƙarfin juyawa. Yayin da ƙarfi ke haifar da hanzarin layi a cikin abubuwa, juyi yana haifar da hanzarin kusurwa a cikin jikin da ke juyawa. Ana ƙididdige juyi a matsayin samfurin ƙarfin da aka yi amfani da shi da kuma nisan da ke tsaye daga axis na juyawa zuwa wurin amfani da ƙarfin.
Menene alaƙar da ke tsakanin hanzarin kusurwa, ƙarfin juyi, da lokacin inertia?
- amsa: An bayar da dangantakar ta hanyar dokar Newton ta biyu don juyawa: $τ = I α$ , inda $τ$ shine ƙarfin juyi, $I$ shine lokacin inertia, kuma $α$ shine hanzarin kusurwa.
Idan lokacin inertia na abu mai juyawa ya ƙaru yayin da ƙarfin juyi na waje ya kasance iri ɗaya, me zai faru da hanzarin kusurwa?
- amsa: Idan lokacin inertia ya ƙaru kuma ƙarfin juyi na waje ya kasance iri ɗaya, hanzarin kusurwa zai ragu.
Ta yaya ra'ayoyin motsin layi da motsin kusurwa suke kama da juna a cikin motsin layi da na juyawa?
- amsa: Motsin layi (wanda aka bayar ta hanyar $p = m v$ , inda $m$ taro ne kuma $v$ shine saurin gudu) shine samfurin mass da linear speed, yayin da angular momentum (wanda aka bayar ta hanyar $L = I ω$ , inda $I$ shine lokacin inertia da kuma $ω$ shine saurin kusurwa) shine samfurin lokacin inertia da saurin kusurwa.
Me ake nufi da kiyaye ƙarfin kusurwa?
- amsa: Kiyaye ƙarfin kusurwa ya nuna cewa idan babu ƙarfin juyawa na waje, jimlar ƙarfin kusurwa na tsarin rufewa yana nan daram.
Me yasa masu wasan tsere kan kankara ke juyawa da sauri idan suka ɗaga hannayensu yayin juyawa?
- amsa: Lokacin da masu wasan tsere kan kankara suka ɗaga hannayensu, suna rage lokacin da suke yin gudu. Saboda kiyaye saurin kusurwa, lokacin da lokacin gudu ya ragu, saurin kusurwa (ko saurin juyawa) dole ne ya ƙaru don kiyaye saurin kusurwar ya kasance iri ɗaya.
Ta yaya kuzarin motsi na juyawa na wani abu yake kwatanta da kuzarin motsi na layi?
- amsa: Ƙarfin motsi na juyawa (wanda aka bayar da 1/2 $I ω^{2}$ ) yayi kama da makamashin motsi na layi (wanda aka bayar da 1/2) $m v^{2}$ ) Na farko yana da alaƙa da juyawar abu, na biyu kuma yana da alaƙa da motsi mai layi.
Shin abu zai iya samun kuzarin motsi na juyawa da na layi a lokaci guda?
- amsa: Eh, abu yana iya samun kuzarin motsi na juyawa da na layi. Misali, tayar birgima tana da kuzarin motsi na juyawa saboda karfin juyawa da kuma karfin motsi na layi saboda motsin gaba.
Idan radius na tayoyin da ke juyawa ya ninka yayin da yake kiyaye saurin kusurwarsa akai-akai, ta yaya lokacin inertia ɗinsa yake canzawa?

amsa: Ana bayar da lokacin inertia na wani faifai mai ƙarfi da 1/2. $m r^{2}$ , inda $m$ shine taro kuma $r$ shine radius. Idan radius ya ninka kuma nauyin ya kasance daidai, lokacin inertia zai ƙaru da kashi huɗu.