1. Bidh nì le mionaid neo-ghluasadachd de 2 kg m 2 a’ rothladh aig 1 rad/s. Dè a th’ ann am momentum ceàrnach an nì?
Aithnichte:
Mionaid neo-sheasmhachd ( I) = 2 kg m²
Astar ceàrnach ( ω ) = 1 rad/s
A dhìth: Gluasad ceàrnach (L)
fuasgladh:
Foirmle gluasad ceàrnach:
L = I ω
L = momentum ceàrnach (kg m 2 /s), I = moment neo-ghluasadachd (kg m 2 ), ω = astar ceàrnach (rad/s)
An gluasad ceàrnach:
L = I ω = (2)(1) = 2 kg m² /s
[irp]
2. Bidh ulóg siolandair 2 kg le radius de 0.1 m a’ rothladh aig astar ceàrnach seasmhach de 2 rad/s. Dè an gluasad ceàrnach a th’ aig an ulóg?
Aithnichte:
Tomad na ulóige (m) = 2 k g
Radius na ulóige (r) = 0.1 m
Astar ceàrnach (ω) = 2 r ad/s
A dhìth: Gluasad ceàrnach
fuasgladh:
Foirmle mionaid inertia airson siolandair cruaidh:
I = 1/2 mr 2
I = mionaid neo-sheasmhachd (kg m² ) , m = mais (kg), r = radius (m)
Mionaid neo-sheasmhachd:
I = 1/2 (2)(0.1) ² = (1)(0.01) = 0.01 kg m²
An astar ceàrnach:
L = I ω = ( 0.01 )( 2 ) = 0.02 kg m² / s
[irp]
3. Bidh cruinne èideadh 2-kg le radius de 0.2 m a’ rothladh aig 4 rad/s. Dè a th’ ann an gluasad ceàrnach a’ bhàil?
Aithnichte:
Tomad a’ bhàil (m) = 2 kg
Radius a’ bhàil (r) = 0.2 m
Astar ceàrnach (ω) = 4 ra d/s
A dhìth: Gluasad ceàrnach
fuasgladh:
Foirmle mionaid inertia airson cruinne èideadh:
Mise = (2/5) mr 2
I = mionaid t de neo-sheasmhachd (kg m² ) , m = mais (kg), r = radius (m)
Am mionaid inertia airson cruinne aonfhoirmeil:
I = (2/5)(2)(0.2) ² = (4/5)(0.04) = 0.032 kg m²
Momentum ceàrnach na cruinne:
L = I ω = ( 0.032 )( 4 ) = 0.128 kg m² / s
[irp]
4. Bidh mìrean 1 -kg a’ rothladh aig astar ceàrnach seasmhach de 2 rad/s. Dè an astar ceàrnach ma tha radius a’ chearcaill 10 cm?
Aithnichte:
Tomad an nì (m) = 1 k g
Raidio a’ chearcaill (r) = 10 cm = 10/100 = 0.1 m
An astar ceàrnach (ω) = 2 rad/ s
A dhìth: Gluasad ceàrnach
fuasgladh:
Foirmle mionaid inertia airson mìrean:
I = mr² = (1)(0.1) ² = (1)(0.01) = 0.01 kg m²
Momentum ceàrnach:
L = I ω = (0.01)(2) = 0.02 kg m² / s
