Respuesta :
Answer:
Moment of inertia of the system is 289.088 kg.m^2
Explanation:
Given:
Mass of the platform which is a uniform disk = 129 kg
Radius of the disk rotating about vertical axis = 1.61 m
Mass of the person standing on platform = 65.7 kg
Distance from the center of platform = 1.07 m
Mass of the dog on the platform = 27.3 kg
Distance from center of platform = 1.31 m
We have to calculate the moment of inertia.
Formula:
MOI of disk = [tex]\frac{MR^2}{2}[/tex]
Moment of inertia of the person and the dog will be mr^2.
Where m and r are different for both the bodies.
So,
Moment of inertia [tex](I_y_y )[/tex] of the system with respect to the axis yy.
⇒ [tex]I_y_y=I_d_i_s_k + I_m_a_n+I_d_o_g[/tex]
⇒ [tex]I_y_y=\frac{M_d_i_s_k(R_d_i_s_k)^2}{2} +M_m(r_c)^2+M_d_o_g(R_c)^2[/tex]
⇒ [tex]I_y_y=\frac{129(1.61)^2}{2} +65.7(1.07)^2+27.2(1.31)^2[/tex]
⇒ [tex]I_y_y=289.088\ kg.m^2[/tex]
The moment of inertia of the system is 289.088 kg.m^2
The moment of inertia of this system is 289.088 kg. m²
First let's write the given values:
Mass of the platform which is a uniform disk = 129 kg
Radius of the disk rotating about vertical axis = 1.61 m
Mass of the person standing on platform = 65.7 kg
Distance from the center of platform = 1.07 m
Mass of the dog on the platform = 27.3 kg
Distance from center of platform = 1.31 m
To find:
Moment of inertia=?
The moment of inertia can be calculated by using this formula:
[tex]I=\frac{M. R^2}{2}[/tex]
Therefore, moment of inertia of the person and a dog is MR² (the mass and distances differs in both cases)
Moment of inertia ([tex]I_{yy}[/tex]) of the system w.r.t. axis yy is :
[tex]I_{yy}=I_{disk}+I_{man}+I_{dog}\\[/tex]
on substituting the values in the above formula we will get:
[tex]I_{yy}=\frac{129.(1.61)^2}{2} +65.7(1.07)^2+27.2(1.31)^2\\\\I_{yy}=289.088kg.m^2[/tex]
The moment of inertia of this system is 289.088 kg. m²
Learn more:
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