Respuesta :
Answer:
The moment of inertia about the rotation axis is 145.35 kg.m²
Explanation:
Given:
Mass of each seat = 6.4 kg
length of rods attached to the seat = radius of the seat from center = 1.5m
Moment of inertia = M₁r²
Moment of inertia about the first child:
total mass at that point = mass of the child + mass of the seat
= 16kg + 6.4 kg = 22.4 kg
Moment of inertia at the point where the first child sits = 22.4 *1.5²
= 50.4 kg.m²
Moment of inertia about the second child:
total mass at that point = mass of the child + mass of the seat
= 23kg + 6.4 kg = 29.4 kg
Moment of inertia at the point where the second child sits = 29.4 *1.5²
= 66.15 kg.m²
Moment of inertia about the two empty seats:
Moment of inertia about the two seats = 2(6.4*1.5²)
= 28.8 kg.m²
Moment of inertia about the rotation axis = Moment of inertia about the point of two children + moment of inertia about the two seat
= (50.4 + 66.15 + 28.8) kg.m²
= 145.35 kg.m²
Therefore, the moment of inertia about the rotation axis is 145.35 kg.m²
The moment of inertia about the rotation axis is 145.35 kgm2.
How do you calculate the moment of inertia?
Given that the mass m_s of the seat is 6.4 kg, length r of the rod is 1.5 m. The masses of two children is m1 = 16 kg and m2 = 23 kg.
The moment of inertia about the first child is calculated given below.
[tex]MI _1 = (m_s+m_1)r^2[/tex]
[tex]MI_1 = (6.4+16)\times 1.5^2[/tex]
[tex]MI_1 = 50.4 \;\rm kg m^2[/tex]
The moment of inertia about the second child is calculated given below.
[tex]MI _2= (m_s+m_2)r^2[/tex]
[tex]MI_2 = (6.4+23)\times 1.5^2[/tex]
[tex]MI_2 = 66.15 \;\rm kg m^2[/tex]
The moment of inertia about the two empty seats is calculated given below.
[tex]MI_s = 2(m_sr^2)[/tex]
[tex]MI_s = 2 ( 6.4\times 1.5^2)[/tex]
[tex]MI_s = 28.8 \;\rm kgm^2[/tex]
The moment of inertia about the rotation axis is the total sum of the moment of inertia about the point of two children and the moment of inertia about the two seats.
[tex]MI = MI_1 +MI_2+MI_s[/tex]
[tex]MI = 50.4 + 66.15 + 28.8[/tex]
[tex]MI = 145.35 \;\rm kgm^2[/tex]
Therefore, the moment of inertia about the rotation axis is 145.35 kgm2.
To know more about the moment of inertia, follow the link given below.
https://brainly.com/question/6953943.
