In an experiment, a solid, uniform cylinder of unknown radius \( R \) and unknown rotational inertia \( I_0 \) about a central axle is initially at rest. A light string is wrapped around the cylinder, as shown in the figure. The string is pulled with a constant unknown force \( F_0 \), causing the cylinder to rotate. After an unknown time interval \( \Delta t_0 \), the string is completely unwound from the cylinder and loses contact with it. To collect data, a student has access to a meterstick, stopwatch, and force probe. The cylinder may rotate but cannot be moved off of its axle. Indicate whether the force applied to the cylinder \( F_0 \) and the rotational inertia of the cylinder \( I_0 \) can be measured directly or calculated from measured quantities.