We introduce Vysics, a vision-and-physics framework for a robot to build an expressive geometry and dynamics model of a single rigid body, using a seconds-long RGBD video and the robot's proprioception. While the computer vision community has built powerful visual 3D perception algorithms, cluttered environments with heavy occlusions can limit the visibility of objects of interest. However, observed motion of partially occluded objects can imply physical interactions took place, such as contact with a robot or the environment. These inferred contacts can supplement the visible geometry with "physible geometry," which best explains the observed object motion through physics. Vysics uses a vision-based tracking and reconstruction method, BundleSDF, to estimate the trajectory and the visible geometry from an RGBD video, and an odometry-based model learning method, Physics Learning Library (PLL), to infer the "physible" geometry from the trajectory through implicit contact dynamics optimization. The visible and "physible" geometries jointly factor into optimizing a signed distance function (SDF) to represent the object shape. Vysics does not require pretraining, nor tactile or force sensors. Compared with vision-only methods, Vysics yields object models with higher geometric accuracy and better dynamics prediction in experiments where the object interacts with the robot and the environment under heavy occlusion. Project page: https://vysics-vision-and-physics.github.io/