A spherical balloon is made from a material whose mass is 2.27 kg. The thickness of the material is negligible compared to the 2.25-m radius of the balloon. The balloon is filled with helium (He) at a temperature of 291 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m3. Find the absolute pressure of the helium gas.

Aperson stands on a platform, initially at rest, that can rotate freely without friction. the moment of inertia of the person plus the platform is ip. the person holds a spinning bicycle wheel with its axis horizontal. the wheel has moment of inertia iw and angular velocity ωw. take the ωw direction counterclockwise when viewed from above. part a what will be the angular velocity ωp of the platform if the person moves the axis of the wheel so that it points vertically upward?