Question

a playground toy has four seats. each 5.0 kg, attached to very light, 1.5-m- long rods, as seen from above in the figure. if two children, with masses of 15 kg and 20 kg, sit in seats opposite one another, what is the moment of inertia about the rotation axis?

Answer 1

To find the moment of inertia about the rotation axis for the playground toy with two children sitting opposite each other, calculate the individual moments of inertia for each child with the formula I = m*r^2 and sum them up to get the total.

Step-by-step explanation:

The question pertains to calculating the moment of inertia for a playground toy, which is conceptually similar to a merry-go-round scenario in physics. To calculate the moment of inertia of the system, you must consider both the moment of inertia for the individual seats and the children sitting on them.

In this case, you have a playground toy with four seats each with a mass of 5.0 kg and rods with a length of 1.5 meters. Two children with masses of 15 kg and 20 kg are sitting opposite one another. The moment of inertia (I) for each seat and child is calculated using the formula I = m*r^2, where m is the mass and r is the distance from the rotation axis. Since the seats are on very light rods, their mass contribution to the moment of inertia is negligible. Therefore, you calculate the moment of inertia for each child using the formula provided and sum the two to find the total moment of inertia for the system.

The calculation is as follows:

• For the 15 kg child: I = 15 kg * (1.5 m)^2 = 33.75 kgm^2
• For the 20 kg child: I = 20 kg * (1.5 m)^2 = 45 kgm^2
• Total moment of inertia: I = I1 + I2 = 33.75 kgm^2 + 45 kgm^2 = 78.75 kgm^2