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The problem of a planar rigid body, with unknown rotational inertia and an unknown input nonlinearity, tracking a desired angular velocity trajectory is addressed using adaptive feedback control. First, an adaptive controller is developed for tracking a desired angular velocity command, assuming linearly entering control. Sufficient conditions on the command signal for estimating the inertia are given. To account for an unknown input nonlinearity, a piecewise-linear approximation of the nonlinearity is inverted to obtain improved angular velocity tracking and inertia identification. Finally, a direct adaptive algorithm, incorporating feedback linearization is proposed, and Lyapunov analysis is used to show convergence of the angular velocity and inertia estimate errors. The approach is validated by experimental implementation.