Torque acting on Satellite, why isn't omega increasing?

[HoosierDaddy]

Torque acting on Satellite, why isn't omega increasing?

Hey guys,

HW help problem here, we have a satellite rotating at some constant angular rate, and we are asked to calculate the torque required to maintain said motion. I am able to do this, given the principal Moments of Inertia for the satellite and knowing what my angular rate is. The torque require then equals the cross product of angular rate and the angular moment vectors.

My problem is this: A torque is acting on the satellite, so why isn't the rotational rate increasing in magnitude?

Any help is appreciated, I have some ideas, but not sure exactly, looking for confimation, etc. My ideas: the applied torque is changing the magnitudes of the angular rate, thus giving the satellite an "off-axis" rotation as it moves through space. Also, thinking something with the Earth's gravity gradient and center of mass and center of gravity opposing this torque, not so sure about the second one.

Thanks again

 

[AndyW]

for any help!

Hello,

It's great that you were able to calculate the torque required to maintain the satellite's rotational motion. As for your question about why the rotational rate is not increasing in magnitude, there are a few factors at play here.

Firstly, it's important to understand that torque is not the only factor that affects the rotational rate of a satellite. In addition to torque, there are other forces acting on the satellite, such as the Earth's gravity and atmospheric drag, that can also affect its rotational motion. These forces can either oppose or assist the torque, resulting in a net change in the satellite's rotational rate.

Furthermore, the satellite's principal moments of inertia and angular momentum also play a role in determining its rotational rate. If the satellite has a large moment of inertia, it will require a larger torque to change its rotational rate. Similarly, if the satellite has a large angular momentum, it will be more resistant to changes in its rotational rate.

In addition, as you mentioned, the Earth's gravity gradient can also affect the satellite's rotational motion. This is because the Earth's gravitational pull is not uniform across the satellite's body, causing a torque that can either oppose or assist the applied torque.

Overall, there are many factors that contribute to the satellite's rotational motion, and it's important to consider all of them in order to fully understand why the rotational rate is not increasing in magnitude. I hope this helps clarify your thoughts and gives you a better understanding of the situation. Best of luck with your homework problem!