Answer:33 * (d/2)^2.
Step-by-step explanation:
To calculate the moment of inertia for a system of two children sitting in seats opposite one another, we need to consider the individual moments of inertia and then apply the parallel axis theorem.
Let's denote the mass of the first child as m1 (13 kg) and the mass of the second child as m2 (20 kg).
The moment of inertia for each child can be calculated using the formula:
I = m * r^2
Where:
I is the moment of inertia,
m is the mass of the child, and
r is the distance from the rotation axis to the child.
Since the children are sitting opposite each other, the axis of rotation would be located between them. Assuming the distance between the children is d, the distance from the rotation axis to each child is d/2.
Therefore, the moment of inertia for the first child (I1) would be:
I1 = m1 * (d/2)^2
Similarly, the moment of inertia for the second child (I2) would be:
I2 = m2 * (d/2)^2
To find the total moment of inertia for the system, we sum the individual moments of inertia:
Total moment of inertia = I1 + I2
Let's substitute the given values into the formulas:
I1 = 13 kg * (d/2)^2
I2 = 20 kg * (d/2)^2
Total moment of inertia = 13 kg * (d/2)^2 + 20 kg * (d/2)^2
Simplifying further:
Total moment of inertia = (13 + 20) * (d/2)^2
= 33 * (d/2)^2
So, the moment of inertia about the rotation axis for the system of two children would be 33 * (d/2)^2.