Got a doosie here, Angular acceleration, time and radius.

[GRice40]

Homework Statement

An Earth satellite moves in a circular orbit with an orbital speed of 6200 m/s. Find the time of one rotation as well as the radial acceleration of the satellite in orbit.

Homework Equations

Ac= V^2/R
mAc=mg
V= 2(pi)R/t

The Attempt at a Solution

Ok, I've gone every which way I can with this problem. I don't know how to go about it. I've drawn an FBD and the only forces I can see acting on it are the weight of the satellite and the Ac. I don't know if there is supposed to be another variable that is assumed, like the radius of the earth, or if gravity acts upon the satellite at 9.8 m/s^2 like it would on earth...I'm pretty lost here. Any advice on how to start?

 

[flyingpig]

I believe the orbital speed is the tangential speed of the satellite.

What is one rotation? (quickly, go back to your unit circle!)

 

[GRice40]

One rotation is 2(pi) radians, iirc.

 

[GRice40]

I still don't know where to go from there, it seems like I need another variable somehow...

 

[rwisz]

I would recommend starting by identifying the known variables and equations that relate to the problem. In this case, we know the orbital speed of the satellite (6200 m/s) and we can use the equation V= 2(pi)R/t to relate it to the time of one rotation (t). We also know that the radial acceleration (Ac) can be calculated using the equation Ac= V^2/R.

Next, we can consider the forces acting on the satellite. As you mentioned, the only forces we need to consider are the weight of the satellite and the centripetal force (Ac). The weight of the satellite can be calculated using the equation mAc=mg, where m is the mass of the satellite and g is the acceleration due to gravity (which is 9.8 m/s^2 on Earth).

To find the time of one rotation, we can rearrange the equation V= 2(pi)R/t to solve for t. Then, we can plug in the given values for V and R to find the time. To find the radial acceleration, we can use the equation Ac= V^2/R and plug in the given values for V and R.

I hope this helps guide you in solving the problem. Remember to always start by identifying the known variables and equations, and then think about the forces at play. Good luck!