Maximum deliverable angular acceleration and torque of motor due to a load
$$M_{mot} = M_{load} + J\alpha +F\Omega$$
Where \$M_{mot}\$ is torque delivered by the motor,  \$M_{load}\$ is the load torqe, \$J\$ is the system moment of inertia: motor rotor + load, \$\alpha\$ is the angular acceleration, \$F\$ is the friction constant, \$\Omega\$ is the angular velocity.