Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.60 m. The merry‑go‑round is spinning at 24.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. What is the equation of the total moment of inertia? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.

In positive numbers less than 1, the zeros between the decimal point and non zero are significant

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?