My daughters are in competition cheerleading and I am having trouble getting the shots I want. It is usually well lit on stage, but not from where we stand to watch her. I want to get the crisp action shots as they tumble across the stage. I have a Nikon D7000, so I know my lens is most likely the issue from getting the shots I want. I currently have the 18-105 kit lens. I have a 50 1.8 as well but prefer a little zoom option since they are not in the same place on the mat all the time. Any recommendations? I don't have a mint to spend, but don't mind spending a little.
What's spending "a little?"
Problem is, you are in low light. The way to compensate for low light are to:
1. Increase aperture. (1.8 is a large aperture... Your lens, at 105mm, has a maximum aperture of 5.6, which is pretty small. So you are probably already at your maximum aperture, which just isn't large enough).
2. Decrease shutter speed. Your camera is doing this -- but slow shutter speed makes for blurry action.
3. Increase ISO. This leads to grainier shots, and your camera may have already maxed out on ISO.
A new lens won't affect shutter speed or ISO directly. Instead, a different lens can have a larger aperture. By having a larger aperture, it can get away with faster shutter speed and lower ISO.
Your 50/1.8 is a very large aperture, so works well if you get close enough.
But telephoto lenses with large aperture are very very expensive.
The standby lens for people in your situation is the 70-200/2.8. For such a lens, even used/off brand, will easily run you $500-$1000. For a "new" Nikon branded 70-200/2.8, you are looking at $2,000+
A more affordable option could be a long prime lens, like a Nikon 180/2.8, but even that is $400-$500 used.
But your basic budget telephoto zoom lenses will all be small aperture (5.6-6.3) lenses, so they will all be equally bad for capturing the low light action you seek.
Your best bet is to use you 50/1.8 and try to get close, or crop later.