Aplayground toy has four seats, each 6.4kg , attached to very light rods of length r= 1.5m , as seen from below in the figure.
if two children, with masses of 16kg and 23kg , sit in seats opposite one another, what is the moment of inertia about the rotation axis?

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

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.