A video may be captured by an image capture device in motion. A stabilized view of the video may be generated by providing a punchout of the video. The punchout of the video may compensate for rotation of the image capture device during capture of the video. The size of the punchout of the video may be changed based on different rotational positions of to provide a view that includes different extents of the captured visual content. The changes in the size of the punchout may simulate changes in zoom of the visual content.