Mìrean mionaid inertia agus cuirp chruaidh - duilgheadasan agus fuasglaidhean

Mionaid inertia a’ ghràin

1. Ball 100-gram ceangailte ri aon cheann de chorda le fad 30 cm. Dè a’ mhionaid inertie a th’ aig a’ bhall timcheall air ais rothlaidh AB? Na toir aire do mhais a’ chorda.

Aithnichte:

An ais rothlaidh aig AB

Ball mais (m) = 100 gram = 100/1000 = 0.1 kg

An t-astar eadar am ball agus an ais rothlaidh (r) = 30 cm = 0.3 m

A dhìth: Mionaid neo-sheasmhachd a’ bhàil (I)

fuasgladh:

I = mr² ⁼ (0.1 kg)(0.3 m) ^²

I = (0.1 kg)(0.09 ^m² )

I = 0.009 kg ^m²

[irp]

2. Ball 100-gram, m1 _, agus ball 200-gram, m2 _, ceangailte le slat le fad 60 cm. Tha mais na slaite air a leigeil seachad. Tha an ais rothlaidh suidhichte ann am meadhan na slaite. Dè a’ mhionaid inertie aig a’ bhuill timcheall air an ais rothlaidh?

Aithnichte:

Tomad ball 1 (m1 ₎ = 100 gram = 100/1000 = 0.1 kg

An t-astar eadar ball 1 agus ais an rothlaidh (r1 ₎ = 30 cm = 30/100 = 0.3 m

Tomad a’ bhàil (m² ₎ = 200 gram = 200/1000 = 0.2 kg

An t -astar eadar ball 2 agus ais an rothlaidh (r2 ₎ = 30 cm = 30/100 = 0.3 m

A dhìth: mionaid neo-sheasmhachd nam bàlaichean

Freagairt:

I = m1 _/ r1 _/ ² + m2 ^/ _r2 / ₂

I = (0.1 kg)( 0.3 m) ^² + (0.2 kg)( 0.3 m) ^²

I = (0.1 kg)( 0.09 m² ⁾ + (0.2 kg)( 0.09 ^m² )

I = 0.009 kg ^m² + 0.018 kg ^m²

I = 0.027 kg ^m²

[irp]

3. Ball 200-gram, m ₁ agus ball 100-gram, m _2, ceangailte le slat le fad 60 cm. Na toir aire do mhais na slaite. Tha ais an rothlaidh suidhichte aig ball m _2. Dè a’ mhionaid inertia aig na bàlaichean? Na toir aire do mhais na slaite.

Aithnichte:

Tomad ball 1 (m1 ₎ = 200 gram = 200/1000 = 0.2 kg

An t-astar eadar ball 1 agus an ais rothlaidh (r1 ₎ = 60 cm = 60/100 = 0.6 m

Tomad ball 2 (m² ₎ = 100 gram = 100/1000 = 0.1 kg

An t-astar eadar ball 2 agus an ais rothlaidh (r2 ₎ = 0 m

A dhìth: Mionaid neo-sheasmhachd nam bàlaichean

fuasgladh:

I = m1 _/ r1 _/ ² + m2 ^/ _r2 / ₂

I = (0.2 kg)( 0,6 m) ^² + (0.2 kg)(0 ) ^²

I = (0.2 kg)( 0.36 ^m² ) + 0

I = 0.072 kg ^m²

[irp]

4. Tha mais gach bàla 100 gram, ceangailte le corda. Tha fad a’ chorda 60 cm agus leud a’ chorda 30 cm. Dè a’ mhionaid inertia a th’ aig a’ bhàl timcheall air ais an rothlaidh? Na toir aire do mhais a’ chorda.

Aithnichte:

Tomad a’ bhàil = m1 ₌ m2 ₌ m3 ₌ m4 ₌ 100 gram = 100/1000 = 0.1 kg

An t-astar eadar am ball agus an ais rothlaidh (r1 ₎ = 30 cm = 30/100 = 0.3 m

An t-astar eadar ball 2 agus an ais rothlaidh (r2 ₎ = 30 cm = 30/100 = 0.3 m

An t-astar eadar ball 3 agus an ais rothlaidh (r3 ₎ = 30 cm = 30/100 = 0.3 m

An t-astar eadar ball 4 agus an ais rothlaidh (r4 ₎ = 30 cm = 30/100 = 0.3 m

Aithnichte: Mionaid neo-sheasmhachd

fuasgladh:

Mise = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²

I = (0.1 kg)( 0.3 m) ^² + (0.1 kg)( 0.3 m) ^² + (0.1 kg)(0.3 m) ^² + (0.1 kg)(0.3 m) ^²

I = (0.1 kg)( 0.09 m² ⁾ + (0.1 kg)(0.09 m² ⁾ + (0.1 kg)(0.09 m² ⁾ + (0.1 kg)(0.09 ^m² )

I = 0.036 kg ^m²

[irp]

Mionaid inertia nì cruaidh

5. Dè a’ mhionaid inertia aig slat aonfhoirmeil 2 kg a dh’fhaid le fad 2 m? Tha an ais rothlaidh suidhichte ann am meadhan na slaite.

Aithnichte:

Tomad na slaite (M) = 2 kg

Fad na slaite (L) = 2 m

A dhìth: Mionaid neo-sheasmhachd

fuasgladh:

Foirmle na h-ùine inertia nuair a tha an ais rothlaidh suidhichte ann am meadhan na slaite fada èideadh:

I = (1/12) ^ML2

I = (1/12) (2 kg)( 2 m) ^²

I = (1/12) (2 kg)(4 ^m² )

I = (1/12)(8 kg ^m² )

I = 8/12 kg ^m²

I = 2/3 kg ^m²

[irp]

6. Dè a’ mhionaid inertia aig slat aonfhoirmeil 2 kg a dh’fhaid le fad 2 m? Tha an ais rothlaidh suidhichte aig aon cheann den t-slat.

Aithnichte:

Tomad na slaite (M) = 2 kg

Fad na slaite cruaidhe (L) = 2 m

A dhìth: Mionaid neo-sheasmhachd

fuasgladh:

Am foirmle airson a’ mhionaid inertia nuair a tha an ais rothlaidh suidhichte aig aon cheann den t-slat:

I = (1/3) ^ML2

I = (1/3) (2 kg)( 2 m) ^²

I = (1/3) (2 kg)(4 ^m² )

I = (1/3)(8 kg ^m² )

I = 8/3 kg ^m²

[irp]

7. Siolandair cruaidh 10-kg le radius de 0.1 m. Tha an ais rothlaidh suidhichte ann am meadhan an t-siolandair chruaidh, mar a chithear san fhigear gu h-ìosal. Dè a’ mhionaid inertia aig an t-siolandair?

Aithnichte:

Tomad an t-siolandair chruaidh (M) = 10 kg

Radius an t-siolandair (L) = 0.1 m

A dhìth: Am mionaid neo-ghnìomhachd

A dhìth: Am mionaid neo-ghnìomhachd

fuasgladh:

Foirmle na mionaid inertia nuair a tha an ais rothlaidh suidhichte ann am meadhan an t-siolandair:

I = (1/2) MR ²

I = (1/2) (10 kg)(0.1 m) ^²

I = (1/2) (10 kg)(0.01 ^m² )

I = (1/2)(0.1 kg ^m² )

I = 0.05 kg ^m²

8. Cruinne aonfhoirmeil 20-kg le fad 0.1 m. Tha an ais rothlaidh a tha suidhichte aig meadhan na cruinne air a shealltainn san fhigear gu h-ìosal.

Aithnichte:

Tomad na cruinne (M) = 20 kg

Raidio na cruinne (L) = 0.1 m

A dhìth: mionaid neo-sheasmhachd

fuasgladh:

Foirmle na h-ùine inertia nuair a tha an ais rothlaidh suidhichte ann am meadhan na cruinne:

I = (2/5) MR ²

I = (2/5)(20 kg)(0.1 m) ²

I = (2/5)(20 kg)(0.01 ^m² )

I = (2/5)(0.2 kg ^m² )

I = 0.4/5 kg ^m²

I = 0.08 kg ^m²

[irp]

9. Plàta tana ceart-cheàrnach 2-kg le fad 0.5 m agus leud 0.2 m. Tha an ais rothlaidh suidhichte ann am meadhan a’ phlàta ceart-cheàrnaich a chithear san fhigear gu h-ìosal. Dè a’ mhionaid inertia aig a’ cheart-cheàrnach?

Aithnichte:

Tomad a’ phlàta ceart-cheàrnaich (M) = 2 kg

Fad a’ phlàta (a) = 0.5 m

Leud a’ phlàta (b) = 0.2 m

A dhìth: Mionaid neo-ghnìomhachd

fuasgladh:

Foirmle mionaid na h-inert nuair a tha an ais rothlaidh suidhichte ann am meadhan a’ phlàta:

I = (1/12 ) M ( ^a2 + ^b2 )

I = (1/12)(2)(0.5 ² + 0.2 ² )

I = (2/12)(0.25 + 0.04)

I = (1/6)(0.29)

I = 0.29/6 kg ^m²