Final answer:
To find velocity v and current i, one must use the relationship w = v/R for an object rolling without slipping and apply circuit analysis techniques such as Kirchhoff's rules.
Step-by-step explanation:
To find the values of v (velocity) and i (current), we must first understand the relationship between the angular velocity w and the linear velocity v for a rolling object. Here, it's given that the rolling motion is without slipping, which implies that w = v/R, where R is the radius of the cylinder. By substituting this relation into the expressions obtained from the figures, we can calculate the values of v and i at a specific time. Specifically for v, it is noted that there's a graph that shows v as a function of t (time), and its behavior can be analyzed. For the current i, we would typically use Kirchhoff's rules or other circuit analysis techniques to determine its value based on the provided circuit diagram and equations.
For instance, the third equation in Example 21.5 could be verified by substituting the calculated currents I1 and I3 to ensure consistency with the results presented. Likewise, the junction rule could be applied at point a in a given figure to solve for current values in a circuit.