5 mau laʻana o nā nīnau ikehu kinetic rotational
1. He 1 kg m² ka manawa o ka inertia o kahi mea e wili ana ma kahi axis paʻa me ka wikiwiki angular o 2 rad/s. He aha ka ikehu kinetic rotational o ka mea?
Pahana
Ua ʻike ʻia:
Manawa o ka inertia (I) = 1 kg m2
Ka wikiwiki angular (ω) = 2 rad/s
Ua nīnau ʻia: Ikehu kinetic wili (EK)
Pane:
ʻO ke ʻano ikehu kinetic rotation:
EK = 1/2 I ω2
Wehewehe: EK = ikehu kinetic rotational (kg m2/s2), I = ka manawa o ka inertia (kg m2), ω = ka wikiwiki angular (rad/s)
Ikehu kinetic wili:
EK = 1/2 I ω2 = 1/2 (1)(2)2 = 1/2 (1)(4) = 2 Joule
2. He 20 kg ke kaumaha o kahi pulley disc paʻa a he 0,2 mika ka radius. Inā e wili ka pulley ma kona axis ma ka wikiwiki angular mau o 4 rad/kekona, he aha ka ikehu kinetic rotational o ka pulley?
Pahana
Ua ʻike ʻia:
Ke kaumaha o ka pulley disc paʻa (m) = 20 kilokani
ʻO ke kaʻina o ka pulley disc paʻa (r) = 0,2 mika
Ka wikiwiki angular (ω) = 4 radians/kekona
Ua nīnau ʻia: He aha ka ikehu kinetic wili o ka pulley?
Pane:
ʻO ke ʻano hana no ka manawa o ka inertia o kahi diski paʻa inā e wili ia ma kahi axis e like me ka mea i hōʻike ʻia ma ke kiʻi:
ʻO wau = 1/2 mr2
Wehewehe: I = ka manawa o ka inertia (kg m2), m = ka nuipa (kg), r = ka radius (mika)
Manawa o ka inertia o kahi diski paʻa:
ʻO wau = 1/2 (20)(0,2)2 = (10)(0,04) = 0,4 kg m2
Ikehu kinetic wili o ka pulley:
EK = 1/2 I ω2 = 1/2 (0,4)(4)2 = (0,2)(16) = 3,2 Joules
3. He pōpō paʻa me ke kaumaha o 10 kg a me ka radius o 0,1 mika e wili ana a puni kona axis me ka wikiwiki angular o 10 rad/s. E hoʻoholo i ka ikehu kinetic rotational o ka pōpō paʻa!
Pahana
Ua ʻike ʻia:
Ka nuipa o kahi pōpō paʻa (m) = 10 kilokani
Ka laulā o kahi poepoe paʻa (r) = 0,1 mika
Ka wikiwiki angular (ω) = 10 radians/kekona
Ua nīnau ʻia: Ikehu kinetic hakipōpō paʻa wau
Pane:
ʻO ke ʻano hana no ka manawa o ka inertia o kahi pōpō paʻa inā e wili ia ma kahi axis e like me ka mea i hōʻike ʻia ma ke kiʻi:
ʻO wau = (2/5) mr2
Wehewehe: I = ka manawa o ka inertia (kg m2), m = ka nuipa (kg), r = ka radius (mika)
Manawa o ka inertia o kahi poepoe paʻa:
ʻO wau = (2/5)(10)(0,1)2 = (4)(0,01) = 0,04 kg m2
Ka ikehu kinetic wili o kahi poepoe paʻa:
EK = 1/2 I ω2 = 1/2 (0,04)(10)2 = (0,02)(100) = 2 Joules
4. Neʻe kahi ʻāpana me ke kaumaha o 0,5 kilokani i loko o kahi pōʻai me ka wikiwiki angular mau o 2 rad/s. E hoʻoholo i ka ikehu kinetic rotational o ka ʻāpana inā he 10 cm ka radius o ke ala o ka ʻāpana.
Pahana
Ua ʻike ʻia:
Ka nuipa o ka ʻāpana (m) = 0,5 kilokani
Ka laulā o kahi poepoe paʻa (r) = 10 kenimika = 10/100 = 0,1 mika
Ka wikiwiki angular (ω) = 2 radians/kekona
Ua nīnau ʻia: Ikehu kinetic wili o nā ʻāpana
Pane:
ʻO ke ʻano hana no ka manawa o ka inertia o kahi ʻāpana:
ʻO wau = Mr.2 = (0,5)(0,1)2 = (0,5)(0,01) = 0,005 kg m2
Ikehu kinetic wili o nā ʻāpana:
EK = 1/2 I ω2 = 1/2 (0,005)(2)2 = 1/2 (0,005)(4) = (0,005)(2) = 0,01 Joules
5. Hoʻomaka ka wili ʻana o kahi diski cylindrical paʻa like ma kona axis me ka wikiwiki angular o 4 rad/s. ʻO ke kaumaha a me ke radius o ka diski he 1 kg a me 0,5 m. Inā kau ʻia kahi apo me ka nui o 0,2 kg a me ka radius o 0,1 m ma luna o ka diski, kahi e kū pono ana ke kikowaena o ke apo ma luna o ke kikowaena o ka diski, a laila e wili pū ka diski a me ke apo me ka ikehu kinetic rotational o…
Pahana
Ua ʻike ʻia:
Ka nuipa o ka paukūʻolokaʻa paʻa (m1) = 1 kilokani
Ka laulā o kahi cylinder paʻa (r1) = 0,5 mika
Ka wikiwiki kihi o kahi cylinder paʻa (ω1) = 4 rad/s
Ka nui o ke apo (m2) = 0,2 kilokani
Ka laulā o ke apo (r)2) = 0,1 mika
Ua nīnau ʻia: Ka ikehu kinetic rotational o ka cylinder a me ke apo
Pane:
E helu mua i ka wikiwiki angular o ka cylinder a me ke apo:
Manawa o ka inertia o kahi cylinder paʻa: I = 1⁄2 m1 r12 = 1/2 (1)(0,5)2 = (0,5)(0,25) = 0,125 kg m2
Manawa o ka inertia o ke apo: I = mr2 = (0,2)(0,1)2 = (0,2)(0,01) = 0,002 kg m2
Ka manawa o ka inertia o kahi cylinder paʻa a me ke apo (I) = 0,125 + 0,002 = 0,127 kg m2
Ka ikaika kihi hoʻomaka (L1) = Ka ikaika kihi hope loa (L2)
I1 ω1 =I2 ω2
(0,125)(4) = (0,125 + 0,002)(ω2)
(0,5) = (0,127)(ω2)
ω2 = 0,5 : 0,127
ω2 = 4 rad/s
E helu i ka ikehu kinetic rotational o ka cylinder a me ke apo:
EK = 1/2 I ω2 = 1/2 (0,127)(4)2 = (0,127)(8) = 1,016 Joules
