Momentum angular - faʻafitauli ma fofo

1. O se mea faitino e 2 kg m ^{2 lona} taimi e feliuliua'i i le 1 rad/s. O le a le angular momentum o le mea faitino?

Ua iloa:

^{Taimi o le} inertia (I) = 2 kg m²

Saosaoa tulimanu ( ω ) = 1 rad/s

Manaomia: Momentum tulimanu (L)

Fofo:

Fua fa'atatau o le angular momentum:

L = I ω

L = le malosi fa'ata'amilomilo (kg m ² /s), I = le malosi fa'ata'amilomilo (kg m ² ), ω = le saoasaoa fa'ata'amilomilo (rad/s)

O le malosi tulimanu:

L = I ω = (2)(1) = 2 kg m ² /s

2. O se poloki silini e 2- kg le mamafa ma le radius e 0.1 m e feliuliua'i i se saoasaoa angular tumau o le 2 rad/s. O le a le angular momentum o le poloki?

Ua iloa:

Mamafa o le poloki (m) = 2 kilokalama

Fa'alava o le poloki (r) = 0.1 mita

Saosaoa tulimanu (ω) = 2 r ad/s

Manaomia: Momentum tulimanu

Fofo:

Fua fa'atatau o le taimi o le inertia mo le silini malo:

I = 1/2 mr ²

I = le taimi o le inertia (kg m ² ), m = mamafa (kg), r = radius (m)

Taimi o le inertia:

I = 1/2 (2)(0.1) ² = (1)(0.01) = 0.01 kg m ²

O le saoasaoa tulimanu:

L = I ω = ( 0.01 )( 2 ) = 0.02 kg m ² /s

3. O se polo lapotopoto e 2-kg le mamafa ma le radius e 0.2 m e feliuliua'i i le 4 rad/s. O le a le angular momentum o le polo.

Ua iloa:

Mamafa o le polo (m) = 2 kg

Lapo'a o le polo (r) = 0.2 mita

Saosaoa tulimanu (ω) = 4 ra d/s

Manaomia: Momentum tulimanu

Fofo:

Fua fa'atatau o le taimi o le inertia mo le polo tutusa:

I = (2/5) mr ²

I = le taimi t o le inertia (kg m ² ), m = mamafa (kg), r = radius (m)

O le taimi o le inertia mo le polo tutusa:

I = (2/5)(2)(0.2) ² = (4/5)(0.04) = 0.032 kg m ²

O le momentum angular o le sphere:

L = I ω = ( 0.032 )( 4 ) = 0.128 kg m² ^/ s

4. O se fasi mea e 1-kg e feliuliua'i i se saoasaoa fa'ata'amilomilo tumau o le 2 rad/s. O le a le saoasaoa fa'ata'amilomilo pe afai o le radius o le li'o e 10 cm.

Ua iloa:

Mamafa o le mea faitino (m) = 1 kilokalama

O le radius o le li'o (r) = 10 cm = 10/100 = 0.1 m

O le saoasaoa tulimanu (ω) = 2 rad/ s

Manaomia: Momentum tulimanu

Fofo:

Fua fa'atatau o le taimi o le inertia mo vaega:

I = mr ² = (1)(0.1) ² = (1)(0.01) = 0.01 kg m ²

Malosiaga tulimanu:

L = I ω = (0.01)(2) = 0.02 kg m ² /s