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As an intern with an engineering firm, you are asked to measure the moment of inertia of a large wheel, for rotation about an axis through its center. Since you were a good physics student, you know what to do. You measure the diameter of the wheel to be 0.88 m and find that it weighs 280 N . You mount the wheel, using frictionless bearings, on a horizontal axis through the wheel's center. You wrap a light rope around the wheel and hang a 6.32 kg mass from the free end of the rope. You release the mass from rest; the mass descends and the wheel turns as the rope unwinds. You find that the mass has speed 4.0 m/s after it has descended 2.5 m .(a) What is the moment of inertia of the wheel for an axis perpendicular to the wheel at its center?

Respuesta :

Answer:

[tex]I=2.766\ kg.m^2[/tex]

Explanation:

We have:

diameter of the wheel, [tex]d=0.88\ m[/tex]

weight of the wheel, [tex]w_w=280\ N[/tex]

mass of hanging object to the wheel, [tex]m_o=6.32\ kg[/tex]

speed of the hanging mass after the descend, [tex]v_o=4\ m.s^{-1}[/tex]

height of descend, [tex]h=2.5\ m[/tex]

(a)

moment of inertia of wheel about its central axis:

[tex]I=\frac{1}{2} m.r^2[/tex]

[tex]I=\frac{1}{2} \frac{w_w}{g}.r^2[/tex]

[tex]I=\frac{1}{2} \times \frac{280}{9.8}\times 0.44^2[/tex]

[tex]I=2.766\ kg.m^2[/tex]

onyebuchinnaji

The moment of inertia of the wheel for an axis perpendicular to the wheel at its center is 17 kgm².

Acceleration of the mass

The acceleration of the mass is calculated as follows;

v² = u² + 2ad

v² = 0 + 2ad

v² = 2ad

a = v²/2d

a = (4²)/(2 x 2.5)

a = 3.2 m/s²

Angular acceleration of the wheel

α = a/R

where;

  • R is the radius of the wheel = 0.44 m

α = 3.2/0.44

α = 7.27 rad/s²

Torque experienced by the wheel

The torque experienced by the wheel due to rope around it is calculated as follows;

τ = Fr = Iα

I = Fr/α

where;

  • F is the applied force
  • r is the radius of the wheel
  • I is moment of inertia of the wheel

I = (mgr)/α

I = (280 x 0.44)/7.27

I = 17 kgm²

Thus, the moment of inertia of the wheel for an axis perpendicular to the wheel at its center is 17 kgm².

Learn more about moment of inertia here: https://brainly.com/question/3406242

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