Te wā o te korekore o ngā matūriki me ngā tinana pakari – ngā raruraru me ngā otinga

Te wā o te korekore o te matūriki

1. He pōro 100-karamu e hono ana ki tētahi pito o te taura, he 30 cm te roa. He aha te tere o te inertia o te pōro ki te tuaka hurihuri AB? Kaua e aro ki te taumaha o te taura.

Mōhiotia:

Te tuaka hurihuri i AB

Papatipu pōro (m) = 100 karamu = 100/1000 = 0.1 kg

Ko te tawhiti i waenganui i te pōro me te tuaka hurihuri (r) = 30 cm = 0.3 m

E hiahiatia ana: Te wā o te korenga o te pōro (I)

Rongoā:

I = mr ² = (0.1 kg)(0.3 m) ²

I = (0.1 kg)(0.09 ^m² )

I = 0.009 kg ^m²

[irp]

2. He pōro 100-karamu, m1 _, me te pōro 200-karamu, m2 , e honoa ana e te tokotoko he 60 cm te roa. Kāore e arohia _te papatipu o te tokotoko. Kei waenganui o te tokotoko te tuaka hurihuri. He aha te tere o te inertia o te pōro ki te tuaka hurihuri?

Mōhiotia:

Taumaha o te pōro 1 (m1 ₎ = 100 karamu = 100/1000 = 0.1 kg

Ko te tawhiti o te pōro 1 me te tuaka hurihuri (r ₁ ) = 30 cm = 30/100 = 0.3 m

Taumaha o te pōro (m² ₎ = 200 karamu = 200/1000 = 0.2 kg

Ko te tawhiti o te pōro 2 me te tuaka hurihuri (r ₂ ) = 30 cm = 30/100 = 0.3 m

E hiahiatia ana: te wā o te korekore o ngā pōro

Whakautu:

I = m ₁ r ₁ ² + m ₂ r ₂ 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. He pōro 200-karamu, m1 me te pōro 100-karamu, m2 _{, e honoa ana e te tokotoko he 60 cm te roa. Kaua e aro ki te taumaha o te} tokotoko. Kei te pōro m2 te tuaka hurihuri . He aha te tere o te inertia o ngā pōro? Kaua e aro ki te taumaha o te tokotoko_.

Mōhiotia:

Taumaha o te pōro 1 (m1 ₎ = 2 00 karamu = 200/1000 = 0.2 kg

Ko te tawhiti i waenganui i te pōro 1 me te tuaka hurihuri (r ₁ ) = 60 cm = 60/100 = 0.6 m

Taumaha o te pōro 2 (m2 ₎ = 100 karamu = 100/1000 = 0.1 kg

Ko te tawhiti i waenganui i te pōro 2 me te tuaka hurihuri (r ₂ ) = 0 m

E hiahiatia ana: Te wā o te korekore o ngā pōro

Rongoā:

I = m ₁ r ₁ ² + m ₂ r ₂ 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. Ko te taumaha o ia pōro he 100 karamu, he taura hono. Ko te roa o te taura he 60 henimita, ā, ko te whānui o te taura he 30 henimita. He aha te tere o te inertia o te pōro ki te tuaka hurihuri? Kaua e aro ki te taumaha o te taura.

Mōhiotia:

Papatipu o te pōro = m1 ₌ m2 ₌ m3 ₌ m4 ₌ 1 00 karamu = 100/1000 = 0.1 kg

Ko te tawhiti i waenganui i te pōro me te tuaka hurihuri (r ₁ ) = 30 cm = 30/100 = 0.3 m

Ko te tawhiti i waenganui i te pōro 2 me te tuaka hurihuri (r ₂ ) = 30 cm = 30/100 = 0.3 m

Ko te tawhiti i waenganui i te pōro 3 me te tuaka hurihuri (r ₃ ) = 30 cm = 30/100 = 0.3 m

Ko te tawhiti i waenganui i te pōro 4 me te tuaka hurihuri (r ₄ ) = 30 cm = 30/100 = 0.3 m

Mōhiotia: Te wā o te korekore

Rongoā:

I = 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]

Te wā o te korekore o tētahi mea pakari

5. He aha te tere o te inertia o tētahi tokotoko 2-kg te roa, he rite tonu ki te 2 m te roa? Kei waenganui o te tokotoko te tuaka hurihuri.

Mōhiotia:

Taumaha o te tokotoko (M) = 2 kg

Te roa o te tokotoko (L) = 2 m

E hiahiatia ana: Te wā o te korekore

Rongoā:

Ko te tātai o te wā o te korekore ina kei waenganui o te tokotoko roa ōrite te tuaka hurihuri:

I = (1/12) ML ²

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. He aha te tere o te inertia o tētahi tokotoko 2-kg te roa, ā, he 2 m te roa? Kei tētahi pito o te tokotoko te tuaka hurihuri.

Mōhiotia:

Taumaha o te tokotoko (M) = 2 kg

Ko te roa o te tokotoko mārō (L) = 2 m

E hiahiatia ana: Te wā o te korekore

Rongoā:

Ko te tātai mō te wā o te korekore ina kei te pito kotahi o te tokotoko te tuaka hurihuri:

I = (1/3) ML ²

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. He rango totoka 10-kg te taumaha, ko te radius he 0.1 m. Kei waenganui o te rango totoka te tuaka hurihuri, e whakaaturia ana i te ahua i raro nei. He aha te tere o te inertia o te rango?

Mōhiotia:

Taumaha o te rango totoka (M) = 10 kg

Te whānui o te rango (L) = 0.1 m

E hiahiatia ana: Te wā o te korekore

E hiahiatia ana: Te wā o te korekore

Rongoā:

Ko te tātai o te wā o te korekore ina kei waenganui o te rango te tuaka hurihuri:

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. He porowhita ōrite 20-kg te taumaha, ko te roa he 0.1 m. Kei waenganui o te porowhita te tuaka hurihuri e whakaaturia ana i te ahua i raro nei.

Mōhiotia:

Papatipu o te porowhita (M) = 20 kg

Ko te pūtoro o te porowhita (L) = 0.1 m

E hiahiatia ana: he wā o te korekore

Rongoā:

Ko te tātai o te wā o te korekore ina kei waenganui o te porowhita te tuaka hurihuri:

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. He pereti angiangi tapawhā rite ki te 2-kg te taumaha, he 0.5 m te roa, he 0.2 m te whānui. Kei waenganui o te pereti tapawhā rite te tuaka hurihuri e whakaaturia ana i te ahua i raro nei. He aha te tere o te inertia o te tapawhā rite?

Mōhiotia:

Taumaha o te pereti tapawhā (M) = 2 kg

Te roa o te pereti (a) = 0.5 m

Ko te whānui o te pereti (b) = 0.2 m

E hiahiatia ana: Te Wā o te Āhuakore

Rongoā:

Te tātai o te wā o te korekore ina kei waenganui o te pereti te tuaka hurihuri:

I = (1/12 ) M (a ² + b ² )

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