In class, we had a student standing on a platform with their arms outstretched while holding masses. The student was rotated in this position and then pulled their arms in and we observed how their angular velocity changed. For this problem we will assume that the student's torso has a cylindrical (rather than rectangular) cross-section with a radius of r_t =1.2m and mass m_t = 69kg. The student's two arms have a total mass of , a radius of r_a,in = 0.18cm when outstretched, and a radius of when held in. The student holds m_m = 5kg masses in each hand. Treat the student's arms as point masses when held in and as thin rods when outstreched. The student's torso may be modelled as a solid cylinder with a height of h_t =1.7m. Part 1 Draw two diagrams for this problem showing the student before and after bringing their arms in. Part 2 Calculate the total moment of inertia of the student with their arms held in while holding the two masses I_in. Part 3 Calculate the total moment of inertia of the student with their arms outstretched while holding the two masses I_out. Part 4 If it takes the student Δt = 3.2s to fully rotate on a frictionless platform with their arms outstretched, calculate their angular speed ω_out. Part 5 After the student pulls their arms in, calculate their new angular speed ω_in . Part 6 If the student dropped both masses while turning with their arms outstretched, what angular speed ω_massless would they have after letting go of the masses? Part 7 After the student let go of the masses with their arms outstretched, what magnitude of linear momentum P_mass would each mass carry away?
In class, we had a student standing on a platform with their arms outstretched while holding masses. The student was rotated in this position and then pulled their arms in and we observed how their angular velocity changed. For this problem we will assume that the student's torso has a cylindrical (rather than rectangular) cross-section with a radius of r_t =1.2m and mass m_t = 69kg. The student's two arms have a total mass of , a radius of r_a,in = 0.18cm when outstretched, and a radius of when held in. The student holds m_m = 5kg masses in each hand. Treat the student's arms as point masses when held in and as thin rods when outstreched. The student's torso may be modelled as a solid cylinder with a height of h_t =1.7m.
Draw two diagrams for this problem showing the student before and after bringing their arms in.
Calculate the total moment of inertia of the student with their arms held in while holding the two masses I_in.
Calculate the total moment of inertia of the student with their arms outstretched while holding the two masses I_out.
If it takes the student Δt = 3.2s to fully rotate on a frictionless platform with their arms outstretched, calculate their angular speed ω_out.
After the student pulls their arms in, calculate their new angular speed ω_in .
If the student dropped both masses while turning with their arms outstretched, what angular speed ω_massless would they have after letting go of the masses?
After the student let go of the masses with their arms outstretched, what magnitude of linear momentum P_mass would each mass carry away?
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