# Homework Help: Spinning satellite - the velocity in the central mass

1. Sep 26, 2010

### Ante

1. The problem statement, all variables and given/known data

A satellite is spinning clockwise and has four low-mass panels sticking out. A tiny meteor rips through one of the panels and continues in the same direction, but with reduced speed. Afterward, calculate vx and vy components of the center-mass velocity of the satellite. Here is a picture I made in paint that demonstrates the problem. http://img529.imageshack.us/f/satellite.png/

2. Relevant equations
Position of central mass R= total summ of (ri*m)/totalsum of m
vcm= total sum of m*vi/total sum of m

3. The attempt at a solution
Since the question doesnt mention any values I decided to define the values as:

Mass of satellite = 2000kg
Radius of the satellite = 15m

Mass of one panel = 100kg
Radius of the panel = 10m

First, I made a coordinate system, where the origo is in the center of the satellite (so its centermas cancels out). I used the definition of the central mass (I assumed the masses are uniform) to prove the central mass is l/2. I calculated the central mass position with the formula R= total summ of (ri*m)/totalsum of m and showed its position in the center of the satellite. So in my graph, the positions of the panels central mass is the satellites radius + (l/2) where l is the length of the panels.

When the meteor hits one of the panels, it transfer one of its own energies according to momentum conservation $$\Delta$$Psys = $$\Delta$$P1+$$\Delta$$P2= 2, which is proved to the reduced speed of the meteor.

However, I assumed that the meteors effect on the satellites velocity is negligble according to newtons third law. The meteor does go in high speed, but its mass is relative low compared to the satellite, and since it breaks through one of the panels, no "real" collision is happening.

I know that the velocity is vcm= total sum of m*vi/total sum of m which I assumed is the velocity in the X direction? How do I get the velocity in the y-component?