Mmegharị ntụgharị - nsogbu na ngwọta

Mmegharị ntụgharị - nsogbu na ngwọta

torque

1. Ogwe osisi dị sentimita iri anọ n'ogologo. E nwere ike atọ na-arụ ọrụ na ogwe osisi ahụ, F ₁ = 20 N, F ₂ = 10 N, na F ₃ = 40 N nwere ntụziaka na ọnọdụ dịka egosiri na eserese dị n'okpuru. Gịnị bụ ike na-eme ka ogwe osisi ahụ na-agbagharị gburugburu etiti oke nke ogwe osisi ahụ?

A maara:

Ebe etiti nke oke dị n'etiti osisi ahụ.

Ogologo osisi (l) = 140 cm = mita 1.4

Ike 1 (F ₁ ) = 20 N, ogwe aka 1 (l ₁ ) = 70 cm = 0.7 mita

Ike 2 (F ₂ ) = 10 N, ogwe aka 2 (l ₂ ) = 100 cm – 70 cm = 30 cm = 0.3 mita

Ike 3 (F ₃ ) = 40 N, ogwe aka 3 (l ₃ ) = 70 cm = 0.7 mita

Achọsiri ike: Oke ike nke ike

Ngwọta:

Tork 1 na-agbagharị ogwe ahụ n'akụkụ aka nri, yabụ e kenyere akara na-adịghị mma na tork 1.

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

Torketi 2 na-agbagharị ogwe osisi ahụ n'akụkụ aka ekpe, yabụ na-enye torketi 2 akara dị mma.

τ ₂ = F ₂ l ₂ = (10 N)(0.3 m) = 3 N m

Tork nke atọ na-agbagharị ogwe aka elekere, yabụ e kenyere tork nke atọ akara dị mma.

τ ₃ = F ₃ l3 = (40 N)(0.7 m) = -28 N m

Ike net:

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

Oke nke ike ahụ bụ 39 N m. Ntụzi nke ntụgharị nke ogwe osisi ahụ na-aga n'ihu n'aka nri, yabụ e kenyere akara na-adịghị mma.

2. Kedu ihe bụ ike ọkụ eletrik na-arụ ọrụ na ogwe ahụ. Axis nke ntụgharị na isi D. (sin 53 ^o = 0.8)

A maara:

Axis nke ntụgharị na isi D

F ₁ = 10 N na l ₁ = r ₁ sin θ = (40 cm) (mmehie 53 ^o ) = (0.4 m) (0.8) = 0.32 mita

F ₂ = 10√2 N na l ₂ = r ₂ mmehie θ = (20 cm) (mmehie 45 ^o ) = (0.2 m) (0.5√2) = 0.1√2 mita

F ₃ = 20 N na l ₃ = r ₁ sin θ = (10 cm) (mmehie 90 ^o ) = (0.1 m) (1) = 0.1 mita

Achọrọ: torque net

Ngwọta:

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

(Torki 1 na-agbagharị ogwe aka ahụ n'akụkụ aka ekpe ya mere anyị na-enye akara dị mma na torki 1)

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

(Torki 2 na-agbagharị ogwe aka elekere aka ya mere anyị na-enye akara ọjọọ na torki 2)

τ ₃ = F ₂ l ₂ = (20 N) (0.1 m) = 2 Nm

(Torki 3 na-agbagharị ogwe aka ahụ n'akụkụ aka ekpe ya mere anyị na-enye akara dị mma na torki 3)

Ike net:

Στ = τ ₁ – τ ₁ + τ ₃

Στ = 3.2 Nm – 2 Nm + 2 Nm

Στ = 3.2 Nm

3. Gịnị bụ ike ọkụ eletrik ma ọ bụrụ na axis nke ntụgharị na isi D. (sin 53 ^o = 0.8)

A maara:

Axis nke ntụgharị na isi D.

Anya dị n'etiti F ₁ na axis nke ntụgharị (r _AD ) = 40 cm = 0.4 m

Anya dị n'etiti F ₂ na axis nke ntụgharị (r _BD ) = 20 cm = 0.2 m

Anya dị n'etiti F ₃ na axis nke ntụgharị (r _CD ) = 10 cm = 0.1 m

F ₁ = 10 Newton

F ₂ = 10√2 Newton

F3 = _{Newton 20}

Sin 53 ^o = 0.8

Achọrọ: torque net

Ngwọta:

Oge ike 1

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

(Torki 1 na-agbagharị ogwe aka ahụ n'akụkụ aka ekpe ya mere anyị na-enye akara dị mma na torki 1)

Oge nke ike 2

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

(Torki 2 na-agbagharị ogwe aka elekere aka ya mere anyị na-enye akara ọjọọ na torki 2)

Oge nke ike 3

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

(Torki 2 na-agbagharị ogwe aka ahụ n'akụkụ aka ekpe ya mere anyị na-enye akara dị mma na torki 3)

Ike net:

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = 3.2 – 2 + 2

Στ = mita Newton 3.2

Oge nke inertia

4. Ogologo waya = 12 m, l ₁ = 4 m. Eleghara oke waya anya. Gịnị bụ oge inertia nke sistemụ ahụ.

A maara:

Ibu nke A (mA ₎ = 0.2 kg

Ibu nke B (m _B ) = 0.6 kg

Anya dị n'etiti A na axis nke ntụgharị (rA ₎ = mita 4

Anya dị n'etiti B na axis nke ntụgharị (r _B ) = 12 – 4 = mita 8

Achọrọ: Oge nke inertia nke sistemụ ahụ

Ngwọta:

Oge nke inertia nke A

I _A = (m _A )(r _A ² ) = (0.2) (4) ² = (0.2) (16) = 3.2 n'arọ m ²

Oge nke inertia nke B

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

Oge nke inertia nke sistemụ ahụ:

I = I _A + I _B = 3.2 + 38.4 = 41.6 n'arọ m ²

Mgbanwe ntụgharị

5. A na-etinye ike 6-N n'ime eriri e ji eriri kechie gburugburu pulley nke ibu M = 5 kg na radius R = 20 cm. Gịnị bụ ọsọ ọsọ nke pulley ahụ. Pulley ahụ bụ silinda siri ike otu.

A maara:

Ike (F) = 6 Newton

Ibu (M) = 5 kg

Redịọs (R) = 20 cm = 20/100 m = 0.2 m

Achọtara: Ọsọ ọsọ akụkụ (α)

Ngwọta:

Oge ike ahụ:

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

Oge nke inertia maka silinda siri ike:

I = 1/2 MR ²

I = ọkara (5 kg)(0.2 m) ²

I = 1/2 (5 kg)(0.04 m ² )

I = 1/2 (0.2)

I = 0.1 kg m ².

Ọganihu akụkụ:

τ = M α

α = τ / I = 1.2 / 0.1 = 12 rad s ^-2

6. Bọlọgụ nke ibu = kilogram 4 nke kwụgidere n'eriri nke gbara gburugburu pulley nke ibu = kilogram 8 na radius R = 10 cm. Ọsọ ọsọ nke ike ndọda bụ 10 ms ^-2 . Gịnị bụ ọsọ ọsọ nke blọk ahụ? Pulọọ ahụ bụ silinda siri ike otu.

A maara:

Ibu nke pulley (m) = 8 kg

Radius nke pulley (r) = 10 cm = 0.1 m

Ibu nke blọk (m) = 4 kg

Ọsọ ọsọ nke ike ndọda (g) = 10 m/s ²

Ibu (w) = mg = (4 kg)(10 m/s ² ) = 40 kg m/s ² = 40 Newtons

Achọsiri ike: Ọsọ ọsọ nke ngọngọ ahụ n'efu

Ngwọta:

Oge nke inertia nke silinda siri ike:

I = 1/2 MR ² = 1/2 (8 kg)(0.1 m) ² = (4 kg)(0.01 m ² ) = 0.04 kg m ²

Oge ike ahụ:

τ = F r = (40 N) (0.1 m) = 4 Nm

Ọganihu akụkụ:

Στ = M α

4 = 0.04 α

α = 4 / 0.04 = 100

Ọsọ ọsọ ahịrị:

a = r α = (0.1) (100) = 10 m/s ²

7. Blọk nwere oke m nke kwụgidere n'elu eriri e ji eriri kechie. Ọ bụrụ na ọsọ ọsọ nke blọk ahụ bụ am/s ² , kedu oge nke inertia nke blọk ahụ..

A maara:

ibu = w = mg

Ogwe aka = R

Ọganihu akụkụ = α

Ọsọ ọdịda efu nke ngọngọ ahụ = a ms ^-2

Achọtara: Oge nke inertia nke pulley (I)

Ngwọta:

Njikọ dị n'etiti osooso ahịrị na osooso angular:

a = Rα

α = a / R

Oge nke inertia:

τ = M α

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

Ike akụkụ

8. Mkpụrụ ndụ gram 0.2 na-agagharị n'ime okirikiri na ọsọ na-agbanwe agbanwe nke m10/s. radius nke okirikiri ahụ bụ 3 cm. Kedu ihe bụ ọsọ nkuku nke mkpụrụ ndụ ahụ?

A maara:

Ibu nke ihe dị n'ime ya (m) = 0.2 gram = 2 x 10 ^-4 kg

Ọsọ akụkụ (ω) = 10 rad s ^-1

Redịọs (r) = 3 cm = 3 x 10 ^-2 mita

Achọsiri ike: Ike akụkụ nke ihe ahụ

Ngwọta:

Usoro nke momentum angular:

L = M ω

I = ike ntụgharị, I = oge nke inertia, ω = ọsọ ntụgharị

Oge nke inertia (maka ihe ndị dị n'ime):

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

Ike nke akụkụ:

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

1. Gịnị bụ mmegharị ntụgharị?
   • Azịza: Njem ntụgharị na-ezo aka na mmegharị nke ihe gbara okirikiri edobere. Ọ bụ ụdị mmegharị nke isi ihe ọ bụla dị na ihe ahụ na-agagharị n'okirikiri gburugburu axis ahụ.
2. Kedu ka ọsọ ahịrị si metụta ọsọ angular na mmegharị ntụgharị?
   • Azịza: Ọsọ kwụ ọtọ ($v$) nke isi ihe dị na ihe na-agbagharị bụ kpọmkwem nhata na anya ya ($r$) site na axis nke ntụgharị na ọsọ akụkụ ($\omega$) nke ihe ahụ. Mmekọrịta ahụ bụ site na $v=r\cdot \omega$.
3. Kedu oge nke inertia, oleekwa otú o si metụta mmegharị ntụgharị?
   • Azịza: Oge nke inertia bụ ihe atụ nke ntụgharị nke oke na mmegharị ahịrị. Ọ na-atụ ihe iguzogide mgbanwe na ọnọdụ ntụgharị ya. Oge inertia dabere na ma oke nke ihe na nkesa ya ma e jiri ya tụnyere axis nke ntụgharị.
4. Kedu ka iwu mbụ nke mmegharị Newton si emetụta mmegharị ntụgharị?
   • Azịza: Dịka ihe nọ n'usoro mmegharị ahụ na-anọgide na-agagharị ma ọ bụrụ na ike mpụga emee ya, ihe nọ n'usoro mmegharị ahụ ga-anọgide n'ọnọdụ ahụ ma ọ bụrụ na ike mpụga emee ya.
5. Gịnị bụ mkpa nke radius nke gyration?
   • Azịza: radius nke gyration na-enye nha nke nkesa nke oke ihe site na axis nke ntụgharị ya. Ọ na-akọwa n'ụzọ bụ isi otú oke ihe niile dị n'ihe ahụ ga-adị mkpa ka a chịkọta ya ka o wee nwee otu oge nke inertia dị ka nkesa mbụ ahụ.
6. Gịnị bụ angular momentum na kedu ka esi echekwa ya?
   • Azịza: Momentum angular bụ nha nhata ntụgharị nke momentum ahịrị. Ọ bụ ihe sitere na oge inertia nke ihe na ọsọ angular ya. N'ime sistemụ mechiri emechi, momentum angular zuru oke na-adịgide adịgide ma ọ bụrụ na torque mpụga emee ya, nke na-egosi nchekwa nke momentum angular.
7. Kedu ka torque si emetụta mmegharị ntụgharị?
   • Azịza: Torque bụ nha nhata ntụgharị nke ike. Ọ na-akpata mgbanwe na mmegharị ntụgharị nke ihe. Iwu nke abụọ nke Newton nyere mmekọrịta ahụ maka ntụgharị: $\tau =I\cdot \alpha$, ebe $\tau$ bụ ike ahụ, $I$ bụ oge nke inertia na $\alpha$ bụ osooso akụkụ.
8. Kedu ka etiti oke si dị iche na etiti ntụgharị?
   • Azịza: Ọ bụ ezie na ha nwere ike ịdị n'otu, etiti oke bụ ebe a pụrụ iche na oke oke ihe niile dị n'ihe dị iche iche dị n'otu maka ebumnuche nke ịgbakọ na mmegharị ahịrị, ebe etiti ntụgharị bụ isi (ma ọ bụ axis) nke ihe na-agbagharị gburugburu.
9. Kedu ọrụ nke ike centripetal na mmegharị ntụgharị?
   • AzịzaIke centripetal bụ ike net nke na-arụ ọrụ n'ihe na-agagharị n'ụzọ okirikiri, nke a na-eche ihu n'etiti ntụgharị. Ọ bụ ọrụ ya idobe ihe n'ụzọ gbagọrọ agbagọ ma gbochie ya ịgagharị n'ahịrị kwụ ọtọ n'ihi enweghị ike.

10. Kedu ka ike kinetic rotation si ejikọta na oge nke inertia na angular velocity?

    • AzịzaIke kinetic nke na-agbagharị bụ ike sitere na ntụgharị nke ihe gburugburu axis. A na-enye ya site na usoro: KE_{rotational​}=1/2 ​I ω², ebe $I$ bụ oge nke inertia na $\omega$ bụ ọsọ akụkụ.