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At this orbit wouldn't all space junk be traveling at the same speed as the spaceship/satellite transversing it? To be dangerous it should be traveling at a much faster (or slower) rate than the object it is putting in danger. But at this altitude everything should be at the same rate?

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  • $\begingroup$ Only if they're going the same direction too. $\endgroup$ – Steve Oct 14 '16 at 13:29
  • $\begingroup$ @Steve a geosynchronous orbit necessarily matches the direction of Earth's rotation. $\endgroup$ – Emilio M Bumachar Oct 14 '16 at 21:51
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    $\begingroup$ @EmilioMBumachar There could be satellites in different orbits, like a polar orbit, that are at that altitude. The difference in velocities would be tremendous. Perhaps we specifically avoid those orbits, but it could happen. $\endgroup$ – Steve Oct 15 '16 at 15:30
  • $\begingroup$ There is only one geostationary orbit. There are many orbit that cross this geostationary orbit at some point: circular, geosynchronous orbits of every inclination, elliptical orbits. $\endgroup$ – Hobbes Oct 17 '16 at 8:00
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If everything is going in the same orbit, that's true, anything impacting will be a low speed. However, there's a few things to consider.

  1. Two large low-speed objects impacting can cause damage. The best known example of this was the Progress-MIR collision.
  2. Objects in Geostationary orbit don't stay there naturally, it requires fuel to keep them there. They will naturally keep the 24 hour cycle, but will tend to increase their inclination with time. This inclination can be up to 15 degrees. A 15 degree impact at 3 km/s still is a difference of 770 m/s, or faster than a speeding bullet.
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There are orbits which oscillate around a geosynchronous point, which could overlap and cause a collision.

More importantly, however, the amount of geosynchronous positions is limited, and junk and dead satellites hanging around there occupying valuable positions is frowned upon. In accordance with an informal (as best I understand) agreement, most satellites, on reaching the end of their fuel, use the last few drops to depart from the geosynchronous spot.

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