Question

We will again be considering the fictional Hermes spacecraft from Assignment #9. Assume the crew module has a moment of inertia of 1cm-232 × 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 6.37 x 10-9 rad/s 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 θ,-35° 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? The crew module part of the spacecraft is rotating with an angular velocity of wH 0.43 rad/s when a surface transport shuttle approaches it. The shuttle has a mass of m, 1.8 x 106 kg, and has a velocity of v, 18 m/s from a direction that is 125 from the radial axis of the Hermes as shown. It attaches to the docking bay on the trailing edge of the crew module a distance r 15 m from the central axis of the Hermes ship -125° 3. After it is docked, what is the magnitude of the angular velocity of the crew module? What would you feel if you were in the crew compartment of the Hermes when the shuttle docked?

Please ignore numbers 1 and 2. Only solve numbers 3 and 4. Thanks.

Answer 1

Initial Angular momentum I_i = I_cm w_H + m_s v r_bottom r_bottom = r min 55 degree r_bottom = 15 sin 55 degree J_i = 232 times 10^6 times 0.43 + 1.8 times 10^6 times 18 times 15 sin 55 degree J_i = 99.76 times 10^6 + 398.11 times 10^6 kg middot m^2/du J_i = 497.87 times 10^6 kg m^2/sec After docking, total moment of Inertia I_f = I_m + m_s a^2 = 232 times 10^6 + 1.8 times 10^6 times (15)^2 I_f = 637 times 10^6 kg middot m^2/sec \r\n By conservation of Angular momentum L_i = L_f 497.87 times 10^6 = 637 times 10^6 times w w_f = 0.782 rad/sec As Angular velocity has increased so crew will feel outward force due to centrifugal force. As F = mrw^2 F Proportional w^2