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In the diagram, disk 1 has a moment of inertia of 3.4 kg Β· m2 and is rotating in the counterclockwise direction with an angular velocity of 6.1 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular velocity of 9.3 rad/s falls from above onto disk 1. The two then rotate as one in the clockwise direction with an angular velocity of 1.8 rad/s. Determine the moment of inertia, in kg Β· m2, of disk 2.

Respuesta :

Answer:

I = 3.6 kgβ€’mΒ²

Explanation:

Conservation of angular momentum

Let's assume CW is the positive direction

3.4(-6.1) + I(9.3) = 3.4(1.8) + I(1.8)

I(9.3 - 1.8) = 3.4(1.8 + 6.1)

I(7.5) = 3.4(7.9)

I = 3.4(7.9)/(7.5) = 3.5813333333...

shubhamchouhanvrVT

The moment of inertia of the second disk will be Β [tex]I=3.58\ kg-m^2[/tex]

What is moment of inertia?

The moment of inertia is defined as the product of mass of section and the square of the distance between the reference axis and the centroid of the section.

here it is given that

MOI of disk one Β  [tex]I_1=3.4\ kg-m^2[/tex]

Angular velocity Β [tex]w_1=6.1\ \frac{rad}{s}[/tex]

Angular velocity of disk two Β [tex]w=1.8\ \frac{rad}{s}[/tex]

MOI of the disk two [tex]I=?[/tex]

The final angular velocity [tex]w_f= 1.8\ \frac{rad}{sec}[/tex]

Now from the conservation of the momentum the angular momentum before collision will be equal to the angular momentum after collision.

[tex]I_1w_1+I_2w_2=(I_1+I_2)w_f[/tex]

Now put the values in the formula

[tex](3.4\times 6.10)+(I_2\times 9.3)=(3.4+I_2)\times 1.8[/tex]

[tex]I_2=3.58\ kg-m^2[/tex]

Thus the moment of inertia of the second disk will be Β [tex]I=3.58\ kg-m^2[/tex]

To know more about moment of inertia follow

https://brainly.com/question/18721435

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