(a)What is the angular momentum of a figure skater spinning at 3.5rev/s with arms in close to her body,assuming her to be a uniform cylinder with a height of 1.5m,radius of 15cm,and a mass of 55kg?

(a) The angular momentum is the product of the moment of inertia and the angular velocity. The moment of inertia of a uniform cylinder is given by
  I = (m/12)(3r^2 + h^2) = (55 kg/12)(3(.15 m)^2 + (1.5 m)^2) = 10.6219 kg m^2
So the angular momentum is
  Iω = (10.6219 kg m^2)(3.5*2π)/s = 233.587 kg•m^2/s
(b) To stop her in 5 seconds, the needed torque is
  T = Iω/t = (233.587 kg m^2/s)/(5 s) = 46.7174 N•m

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A newton (N) has units of kg•m/s^2, so a newton-meter has units of kg•m^2/s^2.