We will again be considering the fictional Hermes spacecraft from Assignment #9.

Question

We will again be considering the fictional Hermes spacecraft from Assignment #9. Assume the crew module has a moment of inertia of L 232 x 106 kgm2. The necessary angular acceleration of the crew module to spin up to the desired rotational velocity during the first round trip to mars is Cm, 6.37 x 10 rad/s a 1. If it is spun up using a pair of ion thrusters mounted around the perimeter of the crew module, which has a diameter of d 40.0 m and they provide a thrust at an angle of 0t 35o relative to the tangential direction, what magnitude of torque must they provide to the spacecraft to achieve the required angular acceleration? 2. How much force must each thruster provide

Explanation / Answer

1.

Icm = moment of inertia = 232 x 106 kgm2

alpha = angular acceleration = 6.37 x 10-9 rad/s2

torque is given as

Torque = Icm alpha = (232 x 106 ) (6.37 x 10-9) = 1.48 Nm

2.

Torque is also given as

Torque = F d Sintheta

1.48 = F (40) Sin(90 - 35)

F = 0.0452 N

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