Ikehu kinetic rotation - nā pilikia a me nā hoʻonā

1. Loaʻa i kahi mea manawa o ka inertia o 1 kg m² hoʻohuli i ka wikiwiki angular mau o 2 rad/s. He aha ka ikehu kinetic wili o ka mea?

ʻIke ʻia:

ʻO ka manawa o ka inertia (I) = 1 kg m²

ka holo wikiwiki angular (ω) = 2 rad / s

Makemake: ʻO ka ikehu kinetic rotational (KE)

Lōlā:

ʻO ke ʻano o ka ikehu kinetic rotational:

KE = 1/2 ʻI ω²

KE = ka ikehu kinetic rotational (kg m²/s²), ʻo wau = ka manawa o ka inertia (kg m²), ω = ka wikiwiki kihi (rad/s)

ʻO ka ikehu kinetic rotational:

KE = 1/2 I ω² = 1/2 (1)(2)² = 1/2 (1)(4) = 2 Joule

2. He 20-kg kaʻa wili paukūʻolokaʻa me ka radius o 0.2 m e wili ana i ka wikiwiki angular mau o 4 rad/s. He aha ka ikehu kinetic rotational o ka pulley?

ʻIke ʻia:

Ka Mass o ka pulley cylinder (M) = 20kg

ʻO ke anawaena o ka cylinder (r) = 0.2 mika

Ka wikiwiki kihi (ω) = 4 rad/s

Makemake ʻia: He aha ka ikehu kinetic rotational

Hoʻonā;

ʻO ke ʻano o ka manawa o ka inertia o ka cylinder:

I = 1/2 mr²

I = ka manawa o ka inertia (kg m²), m = ka nuipaʻa (kg), r = radius (mika)

ʻO ka manawa inertia o ka pulley cylinder:

ʻO wau = 1/2 (20)(0.2)² = (10)(0.04) = 0.4 kg m²

ʻO ka ikehu kinetic rotational o ka pulley:

KE = 1/2 I ω² = 1/2 (0.4)(4)² = (0.2)(16) = 3.2 Joule

3. A-10 kg pōpō me ka radius o 0.1 ka m hoʻohuli ma kahi wikiwiki mau o 10 rad/s. He aha ka ikehu kinetic o ka pōpō.

ʻIke ʻia:

Ka Mass o ka pōpō (M) = 10 kg

Ka laulā o ka pōpō (r) = 0.1 mika

ʻO ka wikiwiki wikiwiki (ω) = 10 rhoʻolaha

Makemake ʻia: ʻO ka ikehu kinetic rotational

Lōlā:

Ke ʻano o ka manawa o ka inertia:

I = (2/5) Mr.²

I = manawa o ka inertia (kg m²), m = ka nuipaʻa (kg), r = radius (M)

Ka manawa o ka inertia o ka pōpō:

ʻO wau = (2/5)(10)(0.1)² = (4)(0.01) = 0.04 kg m²

ʻO ka ikehu kinetic rotational o ka pōpō:

KE = 1/2 I ω² = 1/2 (0.04)(10)² = (0.02)(100) = 2 Joule

4. A 0.5-e wili ana nā ʻāpana kg i ka wikiwiki angular mau o 2 rad/s. He aha ka ikehu kinetic rotational o ka ʻāpana inā ʻo ka radius o ka pōʻai 10 wm.

ʻIke ʻia:

Ka Mass o ka ʻāpana (M) = 0.5kg

ʻO ke anawaena o ka pōpō (r) = 10 kenimika = 10/100 = 0.1 mika

Ka wikiwiki kihi (ω) = 2 rad/s

Makemake ʻia: ʻO ka ikehu kinetic rotational

Lōlā:

Manawa o ka inertia no nā ʻāpana:

I = Mr.² = (0.5)(0.1)² = (0.5)(0.01) = 0.005 kg m²

ʻO ka ikehu kinetic rotational:

KE = 1/2 I ω² = 1/2 (0.005)(2)² = 1/2 (0.005)(4) = (0.005)(2) = 0.01 Joule