Rigid Body Dynamics
Click and drag on the body to apply a force. Off-center forces create torque, spinning the body. Watch translation and rotation couple together as the shape bounces off walls.
About this lab
A rigid body is an idealization: an object that doesn’t deform under any force. In two dimensions, its motion breaks into two independent parts: translation of the center of mass (governed by Newton’s second law, F = ma) and rotation about the center of mass (governed by the rotational analog, τ = Iα).
When you click and drag on the body, the force you apply generally doesn’t pass through the center of mass. The perpendicular component of the force times the distance from the center creates a torque (τ = r × F), which causes angular acceleration. The same force also accelerates the center of mass linearly. This coupling of translation and rotation is what makes rigid body dynamics rich and surprising.
The moment of inertia (I) plays the role of mass in rotational motion: it determines how hard it is to spin the object. It depends on both the mass and how that mass is distributed. A long thin rod has more rotational inertia about its center than a compact disk of the same mass, because the mass is farther from the axis. Each shape in this simulation uses the correct moment of inertia formula.
Wall collisions apply impulses that change both linear and angular velocity. The exact response depends on where the corner hits and the body’s current rotation—sometimes a wall collision can actually speed up the spin while slowing the translation, or vice versa. Total kinetic energy (translational + rotational) is approximately conserved in bounces.