When a manned craft is sent into space it is necessary to know the mass properties of the system, including the moment of inertia of astronauts on the flight, in order to accurately calculate its trajectory and fuel expenditures. The device in Figure 2.71 is one way to measure an astronaut's moment of inertia. The horizontal platform is pinned at \(O\) and supported a distance \(l\) away by a spring with constant \(k\). When the astronaut is not present, the frequency of small vibration of the platform about \(O\) is measured to be \(f\). When the astronaut is lying on the platform, the frequency of small vibration is measured to be \(f_{a}\).

(a) Find the astronaut's moment of inertia about the \(z\) axis.

(b) Assuming reasonable parameter values for the system and an astronaut of height \(2.0 \mathrm{~m}\), calculate the moment of inertia.

Transcribed Image Text:

k Figure 2.71: System to measure astronaut's moment of inertia.