A pair of identical 1000-kg space pods in outer space are connected to each other by a 900-m-long cable. They rotate about a common point like a spinning dumbbell as shown in the figure. Calculate the rotational inertia of each pod about the axis of rotation. What is the rotational inertia of the two-pod system about its midpoint? Express your answers in
The rotational inertia of each pod about the axis of rotation and the rotational inertia of the two-pod system about its midpoint.
Answer to Problem 45A
The rotational inertia of each pod about the axis of rotation is
The rotational inertia of the two-pod system about its midpoint is
Explanation of Solution
Given info:
The mass of the space pods is
The length of the cable is
Formula used:
The expression for the rotational inertia as follows:
Here,
Calculation:
The distance from one end of the cable to its center as follows:
The rotational inertia of each pod about the axis of rotation as follows:
Hence, the rotational inertia of each pod about the axis of rotation is
The rotational inertia of the two-pod system about its midpoint as follows:
Hence, the rotational inertia of the two-pod system about its midpoint is
Conclusion:
Thus, the rotational inertia of each pod about the axis of rotation is
Thus, the rotational inertia of the two-pod system about its midpoint is
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