Question

A space station has a large ring-like component that rotates to simulate gravity for the crew. This ring has a mass M = 2.1×10^5 kg and a radius of R = 86.0 m and can be modeled as a thin hoop. Before spinning up the ring section, crew members Dave and Frank dock their ships, each with mass m = 3.5×10^4 kg on two docking ports located on opposite sides of the center of the ring. The docking ports are located r = 31.0 m from the center of the ring. When the station’s computer begins to spin up the ring it has to spin both the ring and the ships. The ships can be treated as point particles. Two identical thrusters on the edge of the ring are used to spin up the ring with a constant angular acceleration. The ring-ship system takes 3 hours to reach the angular speed at which it simulates Earth’s gravity for the crew on the edge of the ring. What constant force must each of the two thrusters apply to reach this rotational speed?

Answer 1

The moment of inertia of the spaceship+spacestation is

Let the force applied by each thruster is F, the torque on the system is

The applied torque will produce angular acceleration in the system

We will now determine the angular acceleration of the system.

If the spaceship is rotating at an angular speed of , the centrifugal force experienced by the objects at rest relative to the spaceship is

where m' is the mass of the object. This force simulates Earth's gravity

The spaceship should rotate at 0.3377s^-1 angular speed in order to simulate Earth's gravity. If the angular acceleration is constant, the angular speed at time t is given by

The space ship starts from rest and reaches angular speed in

Substituting given values and angular acceleration into equation (1) we get