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Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m, rotate independently around a common axis through their centers. Two of the flywheels rotate in one direction at 8.94 rad/s, but the other one rotates in the opposite direction at 3.42 rad/s.

Required:
Calculate the magnitude of the net angular momentum of the system.

Respuesta :

Answer:

the angular momentum is 1015.52 kg mΒ²/s

Explanation:

given data

mass of each flywheel, m = 65 kg

radius of flywheel, r = 1.47 m

Ο‰1 = 8.94 rad/s

Ο‰2 = - 3.42 rad/s

to find out

magnitude of the net angular momentum

solution

we get here Moment of inertia that is express as

I = 0.5 m rΒ² Β  Β .................1

put here value and we get

I = 0.5 Γ— 65 Γ— 1.47 Γ— 1.47

I = 70.23 kg mΒ²

and

now we get here Angular momentum that is express as

L = I Γ— Ο‰ Β  Β ...........................2

and Net angular momentum will be

L = 2 Γ— I x Ο‰1 - I Γ— Ο‰2

put here value and we get

L = 2 Γ— 70.23 Γ— 8.94 - 70.23 Γ— 3.42

L = 1015.52 kg mΒ²/s

so

the angular momentum is 1015.52 kg mΒ²/s

Cricetus

The magnitude of the net angular momentum of the system will be "1015.52 kg.mΒ²/s".

Momentum

According to the question,

Flywheel's mass, m = 65 kg

Flywheel's radius, r = 1.47 m

ω₁ = 8.94 rad/s

Ο‰β‚‚ = 3.42 rad/s

We know,

The moment of inertia (I),

= 0.5 m rΒ²

By substituting the values,

= 0.5 Γ— 65 Γ— 1.47 Γ— 1.47

= 70.23 kg.mΒ²

hence, The angular momentum be:

β†’ L = I Γ— Ο‰ or,

Β  Β  Β = 2 Γ— I Γ— ω₁ - l Γ— Ο‰β‚‚

Β  Β  Β = 2 Γ— 70.23 Γ— 8.94 - 70.23 Γ— 3.42

Β  Β  Β = 1015.52 kg.mΒ²/s

Thus the above answer is correct.

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