A 50mm lens (or any other focal length you pick) is the same focal length on a crop camera or a full frame.
Perhaps this illustration will help:
This illustration is designed to explain the various crops on different DSLR cameras. While Nikon has only two different size sensors (full frame and a 1.5x crop) Canon has produced three sizes, (full frame, 1.3x crop and 1.6x crop).
The image circle on the left shows the circle projected by a lens designed for a full frame camera and the image circle on the right shows that which would be projected by a lens designed for a crop camera.
The red field of view is that captured by a full frame sensor, the green shows the field captured by a 1.3x sensor and the blue shows the field of view on the 1.6x sensor.
You can see that the mountains within the images captured by the blue fields of view are exactly the same size in both images regardless of the sensor size. That is because a focal length is exactly the same whether it is used on a full frame or a crop camera.
However, you will notice that the full frame "red" sensor will cover a greater area that the "blue" crop sensor. This is what becomes confusing and which makes some photographers think that lenses are of different focal lengths when used on crop and full frame cameras. They are not but, the full frame sensor will cover a wider area than the crop sensor.
If you have a lens designed for a crop camera, it will project an image circle smaller than the image circle projected by the lens designed for the full frame camera. The image projected by a lens designed for a crop camera will not cover a full frame sensor.
I don't know about Nikon but, the EF-S Canon lenses designed exclusively for 1.6x cameras cannot physically fit on a full frame camera. They fit into a camera deeper into the camera and there is a shorter distance between the back of the lens and the sensor than with the EF lenses designed for full frame cameras.
To make this even more confusing, the Tokina 12-24mm and 11-16mm lenses are different animals altogether. Although, they are designed to use with 1.6x crop cameras, they are physically like the EF lenses in how deep they seat into the camera and they can physically fit on full frame cameras. However, the image circle that they project will not cover the entire full frame sensor when used at wider focal lengths and will vignette the image.
Canon Camera/Lens Compatibility
1. Canon EF lenses will physically fit and will work on all Canon DSLR cameras: full frame, 1.3x crop and 1.6x crop
2. Canon EF-S lenses will only physically fit on 1.6x crop canon cameras. Note to muddy the waters even further, they will not physically fit on the original Canon 1.6x crop cameras: D30, D60 and 10D. They will only fit on 20D and later cameras as well as on all Rebels.
3. Tokina 12-24mm and 11-16mm lenses will physically fit on all Canon DSLR cameras but, the image size projected by those lenses will not cover a full frame sensor at wider focal lengths. As an example, I have an old Canon D60 camera which will not accept lenses with EF-S mounts. It will, however, fit my 12-24mm Tokina and since the D60 is a 1.6x crop camera, I can use my 12-24mm Tokina at all focal lengths.