Question

A satellite has a central bus with a moment of inertia of 50 kg-m^2 about its solar array rotation axis. In addition, it has two solar arrays which each have a MOI of 25 kg-m^2 about that axis. If a worst-case, 1 second thruster burn causes an impulse which increases the rotation rate of the full system about this axis by 1 degree/sec, what minimum holding torque would you recommend for each solar array drive?

Answer 1

Answer:

$\tau = 471.2 Nm$

Explanation:

As we know that central bus has moment of inertia as

$I_1 = 50 kg m^2$

also the solar array has moment of inertia given as

$I_2 = 25 kg m^2$

total moment of inertia of the satellite is given as

$I = I_1 + I_2$

$I = 50 + 25 = 75 kg m^2$

now the rotation rate is given as

$\omega = 1 degree/s$

$\omega = 2\pi rad/s$

now the angular acceleration is given as

$\alpha = \frac{\Delta \omega}{\Delta t}$

$\alpha = \frac{2\pi - 0}{1}$

$\alpha = 2\pi rad/s^2$

now torque is given as

$\tau = I\alpha$

$\tau = (75)(2\pi)$

$\tau = 471.2 Nm$