Circles are considered more of a beginner shape for needle turn appliqué, but they can still take a little troubleshooting to get right! If you find that your curves are more pointy than smooth, it may be one of these things causing it.
If you want to head straight to the video tutorial, just scroll to the bottom of this post. Highly recommended, as sometimes these kinds of things are easier to see than read about.
1. Your stitches are too big
If your stitches are too far apart, the curve will be more jagged since it forces you to fold under larger chunky at a time! Switch to smaller, closer together stitches, to make a more gradual curve.
2. Your seam allowance is too big.
The size of your seam allowance is kind of a balancing act. With smaller pieces, you can't cut the seam allowance too large, as it can make it bulky and hard to tuck under. This can make your curve less smooth! Just be sure not to cut it too small, as it can be hard to tuck under without fraying the edge of the fabric.
While I'm sure there are endless possibilities on why your curves aren't smooth, those are the two main factors I've noticed. If you fix both of those things and are still having problems, you can also try tucking the point in with the needle while tugging on the thread.
When sewing on a curve, it's important to just focus on the next quarter of an inch and take your time. And practice, practice, practice!!