Ka neʻe ʻana o ka wili - nā pilikia a me nā hoʻonā

Ka neʻe ʻana o ka wili - nā pilikia a me nā hoʻonā

ʻO Torke

1. He kaola he 140 kenimika ka lōʻihi. ʻEkolu mau mana e hana ana ma ke kaola, ʻo F ₁ = 20 N, F ₂ = 10 N, a me F ₃ = 40 N me ke kuhikuhi a me ke kūlana e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. He aha ka torque e hoʻolilo ai i ke kaola e wili a puni ke kikowaena o ka nuipa o ke kaola?

ʻIke ʻia:

Aia ke kikowaena o ke kaumaha ma ke kikowaena o ke kukuna.

Ka lōʻihi o ke kaola (l) = 140 kenimika = 1.4 mika

Ikaika 1 (F ₁ ) = 20 N, ka lima lever 1 (l ₁ ) = 70 kenimika = 0.7 mika

Ikaika 2 (F ₂ ) = 10 N, ka lima lever 2 (l ₂ ) = 100 kenimika – 70 kenimika = 30 kenimika = 0.3 mika

Ikaika 3 (F ₃ ) = 40 N, ka lima lever 3 (l ₃ ) = 70 kenimika = 0.7 mika

Makemake ʻia: Ka nui o ka torque

Lōlā:

Hoʻohuli ka torque 1 i ke kukuna i ka ʻaoʻao ʻākau, no laila ua hāʻawi ʻia kahi hōʻailona maikaʻi ʻole i ka torque 1.

τ ₁ = F ₁ l ₁ = (20 N)(0.7 m) = -14 N m

Hoʻohuli ka torque 2 i ke kukuna ma ka ʻaoʻao hema, no laila e hāʻawi ana i kahi hōʻailona maikaʻi i ka torque 2.

τ ₂ = F ₂ l ₂ = (10 N)(0.3 m) = 3 N m

Hoʻohuli ka torque 3 i ke kukuna i ka ʻaoʻao ʻākau, no laila ua hāʻawi ʻia kahi hōʻailona maikaʻi i ka torque 3.

τ ₃ = F ₃ l 3 = (40 N)(0.7 m) = -28 N m

ʻO ka torque upena:

Στ = -14 Nm + 3 Nm – 28 Nm = – 42 Nm + 3 Nm = -39 Nm

ʻO ka nui o ka torque he 39 N m. ʻO ke kuhikuhi o ka wili ʻana o ke kukuna i ka ʻaoʻao o ka uaki, no laila ua hāʻawi ʻia kahi hōʻailona maikaʻi ʻole.

2. He aha ka hana a ka torque net ma ke kaola ʻO ke axis o ka rotation ma ke kiko D. (sin 53 ^o = 0.8)

ʻIke ʻia:

ʻO ke axis o ka wili ma ke kiko D

F ₁ = 10 N a me l ₁ = r ₁ hewa θ = (40 knm)(hala 53 ^o ) = (0.4 m)(0.8) = 0.32 mika

F ₂ = 10√2 N a me l ₂ = r ₂ hewa θ = (20 knm)(hala 45 ^o ) = (0.2 m)(0.5√2) = 0.1√2 mika

F ₃ = 20 N a me l ₃ = r ₁ hewa θ = (10 knm)(hala 90 ^o ) = (0.1 m)(1) = 0.1 mika

Makemake ʻia: ʻO ka torque upena

Lōlā:

τ ₁ = F ₁ l ₁ = (10 N)(0.32 m) = 3.2 Nm

(Hoʻohuli ka torque 1 i ke kukuna ma ke ʻano ʻē aʻe no laila ke hāʻawi nei mākou i kahi hōʻailona maikaʻi i ka torque 1)

τ ₂ = F ₂ l ₂ = (10√2 N)( 0.1√2 m) = -2 Nm

(Hoʻohuli ka torque 2 i ke kukuna i ka ʻaoʻao ʻākau no laila ke hāʻawi nei mākou i ka hōʻailona maikaʻi ʻole i ka torque 2)

τ ₃ = F ₂ l ₂ = (20 N)(0.1 m) = 2 Nm

(Hoʻohuli ka torque 3 i ke kukuna ma ke ʻano ʻē aʻe no laila ke hāʻawi nei mākou i kahi hōʻailona maikaʻi i ka torque 3)

ʻO ka torque upena:

Στ = τ ₁ – τ ₁ + τ ₃

Στ = 3.2 Nm – 2 Nm + 2 Nm

Στ = 3.2 Nm

3. He aha ka torque net inā ʻo ke axis o ka wili ma ke kiko D. (sin 53 ^o = 0.8)

ʻIke ʻia:

ʻO ke axis o ka wili ma ke kiko D.

Ka mamao ma waena o F ₁ a me ke axis o ka wili (r _AD ) = 40 cm = 0.4 m

Ka mamao ma waena o F ₂ a me ke axis o ka wili (r _BD ) = 20 cm = 0.2 m

Ka mamao ma waena o F ₃ a me ke axis o ka wili (r _CD ) = 10 cm = 0.1 m

F ₁ = 10 Newton

F ₂ = 10√2 Newton

F3 = 20 _Newtons

Sin 53 ^o = 0.8

Makemake ʻia: ʻO ka torque upena

Lōlā:

ʻO ka manawa o ka ikaika 1

Στ ₁ = (F ₁ )(r _AD hewa 53 ^o ) = (10 N)(0.4 m)(0.8) = 3.2 Nm

(Hoʻohuli ka torque 1 i ke kukuna ma ke ʻano ʻē aʻe no laila ke hāʻawi nei mākou i kahi hōʻailona maikaʻi i ka torque 1)

ʻO ka manawa o ka ikaika 2

Στ ₂ = (F ₂ )(r _BD hewa 45 ^o ) = (10√2 N)(0.2 m)(0.5√2) = -2 Nm

(Hoʻohuli ka torque 2 i ke kukuna i ka ʻaoʻao ʻākau no laila ke hāʻawi nei mākou i ka hōʻailona maikaʻi ʻole i ka torque 2)

ʻO ka manawa o ka ikaika 3

Στ ₃ = (F ₃ )(r _CD hewa 90 ^o ) = (20 N)(0.1 m)(1) = 2 Nm

(Hoʻohuli ka torque 2 i ke kukuna ma ke ʻano ʻē aʻe no laila ke hāʻawi nei mākou i kahi hōʻailona maikaʻi i ka torque 3)

ʻO ka torque upena:

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = 3.2 – 2 + 2

Στ = 3.2 mika Newton

ʻO ka manawa o ka inertia

4. Ka lōʻihi o ke kaula = 12 m, l ₁ = 4 m. E hoʻowahāwahā i ke kaumaha o ke kaula. He aha ka manawa o ka inertia o ka ʻōnaehana.

ʻIke ʻia:

Ka nuipa o A (m _A ) = 0.2 kg

Ka nuipa o B (m _B ) = 0.6 kg

Ka mamao ma waena o A a me ke axis o ka wili (r _A ) = 4 mika

Ka mamao ma waena o B a me ke axis o ka wili (r _B ) = 12 – 4 = 8 mika

Makemake ʻia: ʻO ka manawa o ka inertia o ka ʻōnaehana

Lōlā:

ʻO ka manawa o ka inertia o A

I _A = (m _A )(r _A ² ) = (0.2)(4) ² = (0.2)(16) = 3.2 kg m ²

ʻO ka manawa o ka inertia o B

I _B = (m _B )(r _B ² ) = (0.6)(8) ² = (0.6)(64) = 38.4 kg m ²

ʻO ka manawa o ka inertia o ka ʻōnaehana:

I = I _A + I _B = 3.2 + 38.4 = 41.6 kg m ²

Nā dinamika hoʻohuli

5. Hoʻopili ʻia kahi ikaika 6-N i ke kaula i kāʻei ʻia a puni kahi pulley o ke kaumaha M = 5 kg a me ka radius R = 20 cm. He aha ka wikiwiki angular o ka pulley. He cylinder paʻa like ka pulley.

ʻIke ʻia:

Ikaika (F) = 6 Newton

Nuipaʻa (M) = 5 kg

Radius (R) = 20 kenimika = 20/100 m = 0.2 m

Makemake ʻia: Hoʻolalelale angular (α)

Lōlā:

Ka manawa o ka ikaika:

τ = FR = (6 Newton)(0.2 mika) = 1.2 N m

ʻO ka manawa o ka inertia no ka cylinder paʻa:

ʻO wau = 1/2 MR ²

ʻO wau = 1/2 (5 kg)(0.2 m) ²

ʻO I = 1/2 (5 kg)(0.04 ^m² )

ʻO wau = 1/2 (0.2)

ʻO I = 0.1 kg ^m².

ʻO ka hoʻolalelale angular:

τ = I α

α = τ / I = 1.2 / 0.1 = 12 rad s ^-2

6. He poloka nuipa = 4 kg e kau ana mai ke kaula i wahī ʻia a puni kahi pulley nuipa = 8 kg a me ke radius R = 10 cm. ʻO ka wikiwiki ma muli o ke koʻikoʻi he 10 ms ^-2 . He aha ka wikiwiki linear o ka poloka? He cylinder paʻa like ka pulley.

ʻIke ʻia:

Ka nuipa o ka pulley (m) = 8 kg

ʻO ke kaʻina o ka pulley (r) = 10 kenimika = 0.1 m

Ka nuipa o ka poloka (m) = 4 kg

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s ²

Kaumaha (w) = mg = (4 kg)(10 m/s² ⁾ = 40 kg m/s² ⁼ 40 Newtons

Makemake ʻia: Ka wikiwiki o ka hāʻule manuahi o ka poloka

Lōlā:

ʻO ka manawa o ka inertia o ka cylinder paʻa:

ʻO I = 1/2 MR2 ⁼ 1/2 (8 kg)(0.1 m) ² = (4 kg)(0.01 m2 ⁾ = 0.04 kg ^m2

Ka manawa o ka ikaika:

τ = F r = (40 N)(0.1 m) = 4 Nm

ʻO ka hoʻolalelale angular:

Στ = I α

4 = 0.04 α

α = 4 / 0.04 = 100

ʻO ka hoʻolalelale linear:

a = r α = (0.1)(100) = 10 m/s ²

7. He poloka me ke kaumaha o m e kau ana mai ke kaula i wahī ʻia a puni kahi pulley. Inā ʻo ka wikiwiki o ka hāʻule manuahi o ka poloka he am/s ² , he aha ka manawa o ka inertia o ka pulley..

ʻIke ʻia:

kaumaha = w = mg

Lima lever = R

ʻO ka hoʻolalelale kihi = α

ʻO ka wikiwiki o ka hāʻule manuahi o ka poloka = a ms ^-2

Makemake ʻia: ʻO ka manawa o ka inertia o ka pulley (I)

Lōlā:

ʻO ka pilina ma waena o ka wikiwiki linear a me ka wikiwiki angular:

a = Rα

α = a / R

Ka manawa o ka inertia:

τ = I α

I = τ : α = τ : a / R = τ (R / a) = τ R a ^-1

ʻO ka momentum angular

8. Ke neʻe nei kahi ʻāpana 0.2-gram i loko o kahi pōʻai ma ka wikiwiki mau o 10 m/s. ʻO ke radius o ka pōʻai he 3 cm. He aha ka momentum angular o ka ʻāpana?

ʻIke ʻia:

Ka nuipa o ka ʻāpana (m) = 0.2 gram = 2 x 10 ^-4 kg

Ka wikiwiki kihi (ω) = 10 rad s ^-1

Radius (r) = 3 kenimika = 3 x 10 ^-2 mika

Makemake ʻia: ʻO ka momentum angular o ka ʻāpana

Lōlā:

ʻO ke kaulike o ka momentum angular:

L = I ω

ʻO I = ka momentum angular, ʻo I = ka manawa o ka inertia, ʻo ω = ka wikiwiki angular

ʻO ka manawa o ka inertia (no nā ʻāpana):

ʻO I = mr ² = (2 x 10 ^-4 )(3 x 10 ^-2 ) ² = (2 x 10 ^-4 )(9 x 10 ^-4 ) = 18 x 10 ^-8

ʻO ka momentum angular:

L = I ω = (18 x 10 ^-8 )(10 rad s ^-1 ) = 18 x 10 ^-7 kg m ² s ^-1

1. He aha ka neʻe ʻana o ka wili?
   • paneʻO ka neʻe ʻana o ka mea e puni ana i kahi axis paʻa. ʻO ia ke ʻano o ka neʻe ʻana o kēlā me kēia kiko o ka mea i loko o kahi pōʻai a puni ke axis.
2. Pehea e pili ai ka wikiwiki linear i ka wikiwiki angular i ka neʻe wili ʻana?
   • pane: Ka wikiwiki laina ($v$) o kahi kiko i loko o kahi mea e wili ana ua kūlike pololei ia me kona mamao ($r$) mai ke axis o ka wili a me ka wikiwiki angular ($\omega$) o ka mea. Hāʻawi ʻia ka pilina e $v=r\cdot \omega$.
3. He aha ka manawa o ka inertia, a pehea e pili ai i ka neʻe ʻana o ka rotational?
   • paneʻO ka manawa o ka inertia ka mea like me ka rotational o ka nuipa i ka neʻe linear. Ana ia i ke kū'ē ʻana o kahi mea i nā loli i kona kūlana rotational. Aia ka manawa o ka inertia i ka nuipa o kahi mea a me kona hoʻolaha ʻana e pili ana i ke axis o ka rotation.
4. Pehea e pili ai ke kānāwai mua o ka neʻe ʻana o Newton i ka neʻe ʻana o ka rotation?
   • paneE like me ka mea e neʻe ana ma ke ʻano linear e noho mau ana i ka neʻe ke ʻole e hana ʻia e kahi ikaika o waho, e noho nō kahi mea e neʻe ana ma ke ʻano rotational ma ia kūlana ke ʻole e hana ʻia e kahi torque o waho.
5. He aha ke koʻikoʻi o ka radius o ka gyration?
   • paneʻO ke anawaena o ka gyration e hāʻawi i kahi ana o ka hoʻolaha ʻana o ka nuipa o kahi mea mai kona axis o ka wili ʻana. Hōʻike maoli ia i ka mamao o ka nuipa a pau o ka mea mai ke axis e pono ai ke hoʻopili ʻia e loaʻa ai ka manawa like o ka inertia e like me ka hoʻolaha mua.
6. He aha ka momentum angular a pehea e mālama ʻia ai?
   • paneʻO ka momentum angular ka like o ka rotational o ka momentum linear. ʻO ia ka huahana o ka manawa inertia o kahi mea a me kona wikiwiki angular. I loko o kahi ʻōnaehana pani, e mau ana ka momentum angular holoʻokoʻa ke ʻole e hana ʻia e kahi torque waho, e hōʻike ana i ka mālama ʻana i ka momentum angular.
7. Pehea e hoʻohuli ai ka torque i ka neʻe ʻana o ka rotation?
   • paneʻO Torque ka like o ka wili ʻana o ka ikaika. Hoʻololi ia i ka neʻe wili ʻana o kahi mea. Hāʻawi ʻia ka pilina e ke kānāwai ʻelua o Newton no ka wili ʻana: $\tau =I\cdot \alpha$, kahi $\tau$ ʻo ia ka torque, $I$ ʻo ia ka manawa o ka inertia, a $\alpha$ ʻo ia ka hoʻolalelale angular.
8. Pehea ka ʻokoʻa o ke kikowaena o ka nuipa mai ke kikowaena o ka wili?
   • paneʻOiai hiki iā lākou ke kūlike, ʻo ke kikowaena o ka nuipa kahi e hiki ai ke manaʻo ʻia ua hoʻopili ʻia ka nuipa holoʻokoʻa o kahi mea no ke kumu o ka helu ʻana ma ka neʻe linear, ʻoiai ʻo ke kikowaena o ka wili ʻo ia ke kiko (a i ʻole axis) e wili ai kahi mea.
9. He aha ke kuleana o ka ikaika centripetal i ka neʻe ʻana o ka wili?
   • paneʻO ka ikaika centripetal ka ikaika ʻupena e hana ana ma luna o kahi mea e neʻe ana ma ke ala pōʻai, e kuhikuhi ana i ke kikowaena o ka wili. ʻO ia ke kuleana no ka mālama ʻana i kahi mea ma kona ala piʻo a me ka pale ʻana iā ia mai ka neʻe ʻana ma kahi laina pololei ma muli o ka inertia.

10. Pehea e pili ai ka ikehu kinetic rotational i ka manawa o ka inertia a me ka wikiwiki angular?

    • paneʻO ka ikehu kinetic rotational ka ikehu ma muli o ka wili ʻana o kahi mea e pili ana i kahi axis. Hāʻawi ʻia e ke ʻano hana: KE_{rotational​}=1/2 ​I ω², kahi $I$ ʻo ia ka manawa o ka inertia a $\omega$ ʻo ia ka wikiwiki angular.