The angular momentum of an object can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
In the case of the ballet dancer, we are told that they are spinning at 1.5 rev/sec, and that they can be modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m, and a radius of 0.16 m.
We can calculate the moment of inertia of the cylinder using the formula I = (1/2) MR^2, where M is the mass and R is the radius.
Plugging in the values we have, I = (1/2)(62 kg)(0.16 m)^2 = 3.072 kg-m^2
We can then calculate the angular momentum of the dancer by plugging in the values we have into the formula L = Iω,
L = (3.072 kg-m^2)(1.5 rev/sec) = 4.608 kg-m^2/s
So the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec, modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m is 4.608 kg-m^2/s.