A mass is attached to the end of a string that is wrapped around a pulley fixed on a rotational axis as shown in the figure below. The pulley is in the shape of a disk with a moment of inertia of $I=\frac{1}{2}M{R}^2.$ The system is released from rest at the instant shown below and the string unwraps without slipping. Is the following statement true or false?

As the system moves, the kinetic energy of the system is $\frac{1}{2}m{v}^2+\frac{1}{2}I{}^2,$ where $v$ is the speed of the block and $$ is the angular velocity of the pulley.

True or False?