Question

One example of angular momentum is someone (like Bill Nye, the Science Guy) on a rotating platform. In a regular year we would have done this in lab ourselves, but since we can't - have a video instead. Assume for now we are talking about when he has his arms pulled in towards his torso and not stretched out. Bill Nye has a mass of 84.0 kg, a height of 1.50 m and a radius of 16.0 cm. He is spinning at a rate of 5.00 rpm (revolutions / minute) by the end of the video. What is his angular momentum based on these numbers

Answer 1

‭0.563 kg-m²/s

Step-by-step explanation:

Bill Nye's angular momentum L = Iω where I = rotational inertia = 1/2MR² (since we are considering him to be cylinder with his axis of rotation from is top to bottom- that is vertical through his height) where M = his mass = 84.0 kg and R = his radius = 16.0 cm = 0.16 m and ω = angular speed = 5.00 rpm = 5.00 × 2π/60 = π/6 rad/s = 0.524 rad/s

L = Iω

L = 1/2MR²ω

Substituting the values of the variables into the equation, we have

L = 1/2MR²ω

L = 1/2 × 84.0 kg × (0.16 m)² × 0.524 rad/s

L = 1/2 × 84.0 kg × ‭0.0256‬ m² × 0.524 rad/s

L = 1/2 × ‭1.12681 kg-m²rad/s

L = ‭0.5634 kg-m²rad/s

L ≅ ‭0.563 kg-m²/s