A small satellite may be approximated as a uniform solid sphere with rotational…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A small satellite may be approximated as a uniform solid sphere with rotational inertia 120kg⋅m2 about an axis through its center. The satellite is initially at rest in space. To orient the craft, two separate thrusters fire sequentially about the same axis (taken as the +z axis):
• Thruster A produces a constant 15N⋅m torque in the +z direction for 4.0s.
• Immediately afterward, Thruster B produces a constant torque in the −z direction (opposite sense) for a time interval tB chosen so that the satellite attains a final angular speed of 2.0rad/s in the −z direction (clockwise when viewed from +z).
Neglect any other torques on the system.
(a) Calculate the satellite’s angular momentum immediately after Thruster A ceases firing. Specify magnitude and direction.
(b) Determine the angular impulse that must be delivered by Thruster B to achieve the specified final angular speed.
(c) Using your result from part (b), compute the duration tB for which Thruster B must fire if its torque magnitude is 25N⋅m.
(d) If mission constraints limit Thruster B to a firing time of only 2.0s, calculate the torque magnitude it must produce to reach the same final angular speed. Explain the proportional relationship used in your calculation.