Ihe atụ nke ike kinetic ntụgharị

Ihe atụ ise nke ajụjụ ike kinetic rotation

1. Ihe nwere oge nke inertia 1 n'arọ m² na-agbagharị n'elu axis a kapịrị ọnụ na ọsọ nkuku 2 rad/s. Ego ole ka ọ ga-eri? ike kinetic ntụgharị ihe ahụ?

Mkparịta ụka
A maara na:
Oge nke inertia (I) = 1 kg m²
Ọsọ akụkụ (ω) = 2 rad/s
A jụrụ: Ike kinetic nke ntụgharị (EK)
Azịza:
Usoro ike kinetic nke ntụgharị:
EK = 1/2 I ω²
Nkọwa: EK = ike kinetic ntụgharị (kg m²/s²), I = oge nke inertia (kg m²), ω = ọsọ angular (rad/s)

Ike kinetic nke ntụgharị:
EK = 1/2 I ω² = 1/2 (1)(2)² = 1/2 (1)(4) = 2 Joule

2. Pulley diski siri ike nwere oke ibu nke kilogram 20 na radius nke mita 0,2. Ọ bụrụ na pulley ahụ na-agbagharị n'axis ya na ọsọ nkuku na-agbanwe agbanwe nke 4 rad/sekọnd, kedu ike kinetic nke pulley ahụ?

Mkparịta ụka
A maara na:
Ibu nke pulley diski siri ike (m) = kilogram 20
Radius nke pulley diski siri ike (r) = mita 0,2
Ọsọ akụkụ (ω) = 4 radians/sekọnd
A jụrụ: Kedu ike ntụgharị nke pulley?
Azịza:
Usoro maka oge nke inertia nke diski siri ike ma ọ bụrụ na ọ na-agbagharị n'elu axis dịka egosiri na foto a:
I = 1/2 m²
Nkọwa: I = oge nke inertia (kg m²), m = oke (kg), r = radius (mita)
Oge nke inertia nke diski siri ike:
I = 1/2 (20)(0,2)² = (10)(0,04) = 0,4 kg m²

Ike kinetic nke polley:
EK = 1/2 I ω² = 1/2 (0,4)(4)² = (0,2)(16) = 3,2 Joules

3. Bọọlụ siri ike nke nwere oke kilogram iri na radius nke mita 0,1 na-agbagharị gburugburu axis ya na ọsọ akụkụ nke 10 rad/s. Chọpụta ike kinetic nke bọọlụ siri ike!
Mkparịta ụka
A maara na:
Ibu nke bọọlụ siri ike (m) = kilogram 10
Radius nke okirikiri siri ike (r) = mita 0,1
Ọsọ akụkụ (ω) = 10 radians/sekọnd
A jụrụ: Ike Kinetic ụzọ gasịbọọlụ siri ike m
Azịza:
Usoro maka oge nke inertia nke bọọlụ siri ike ma ọ bụrụ na ọ na-agbagharị n'elu axis dịka egosiri na foto a:
I = (2/5) mr²
Nkọwa: I = oge nke inertia (kg m²), m = oke (kg), r = radius (mita)
Oge nke inertia nke okirikiri siri ike:
I = (2/5)(10)(0,1)² = (4)(0,01) = 0,04 kg m²

Ike kinetic nke okirikiri siri ike:
EK = 1/2 I ω² = 1/2 (0,04)(10)² = (0,02)(100) = 2 Joules

4. Mkpụrụ ndụ ihe nketa nke dị kilogram 0,5 na-agagharị n'ime okirikiri nke nwere ọsọ nkuku na-agbanwe agbanwe nke 2 rad/s. Chọpụta ike kinetic nke mkpụrụ ndụ ihe nketa ahụ ma ọ bụrụ na radius nke ụzọ mkpụrụ ndụ ihe nketa ahụ dị sentimita 10.
Mkparịta ụka
A maara na:
Ibu nke ihe dị n'ime ya (m) = kilogram 0,5
Radius nke okirikiri siri ike (r) = 10 cm = 10/100 = mita 0,1
Ọsọ akụkụ (ω) = 2 radians/sekọnd
A jụrụ: Ike kinetic nke ihe ndị ahụ na-agbanwe agbanwe
Azịza:
Usoro maka oge nke inertia nke ihe dị n'ime:
M = Maazị² = (0,5)(0,1)² = (0,5)(0,01) = 0,005 kg m²
Ike kinetic nke ihe ndị ahụ na-agbanwe agbanwe:
EK = 1/2 I ω² = 1/2 (0,005)(2)² = 1/2 (0,005)(4) = (0,005)(2) = 0,01 Joules

5. Diski siri ike nke nwere otu ụdị cylindrical na-agbagharị na axis ya na ọsọ nkuku nke 4 rad/s. Oke na radius nke diski ahụ bụ 1 kg na 0,5 m. Ọ bụrụ na etinyere mgbanaka nwere oke nke 0,2 kg na radius nke 0,1 m na diski ahụ, ebe etiti mgbanaka ahụ dị kpọmkwem n'elu etiti diski ahụ, mgbe ahụ diski ahụ na mgbanaka ahụ ga-agbagharị ọnụ yana ike kinetic nke…
Mkparịta ụka
A maara na:
Ibu nke silinda siri ike (m₁) = 1 kilogram
Radius nke silinda siri ike (r)₁) = mita 0,5
Ọsọ akụkụ nke silinda siri ike (ω)₁) = 4 rad/s
Oke mgbaaka (m)₂) = 0,2 kilogram
Mgbaaka mgbanaka (r)₂) = mita 0,1
A jụrụ: Ike kinetic nke silinda na mgbanaka
Azịza:
Mbụ gbakọọ ọsọ akụkụ nke silinda na mgbanaka ahụ:
Oge nke inertia nke silinda siri ike: I = 1⁄2 m₁ r₁² = 1⁄2 (1)(0,5)² = (0,5)(0,25) = 0,125 kg m²
Oge nke inertia nke mgbanaka ahụ: I = mr² = (0,2)(0,1)² = (0,2)(0,01) = 0,002 kg m²
Oge nke inertia nke silinda siri ike na mgbanaka (I) = 0,125 + 0,002 = 0,127 kg m²

Ike akụkụ mmalite (L)₁) = Ike ngwụcha akụkụ (L₂)
I₁ ω₁ = M₂ ω₂
(0,125) (4) = (0,125 + 0,002) (ω₂)
(0,5) = (0,127)(ω₂)
ω₂ = 0,5: 0,127
ω₂ = 4 rad/s

Gbakọọ ike ntụgharị nke silinda na mgbanaka:
EK = 1/2 I ω² = 1/2 (0,127)(4)² = (0,127)(8) = 1,016 Joules