In the past lumberjacks would transport logs to the sawmill

In the past, lumberjacks would transport logs to the sawmill by floating them down rivers. Often, workers would walk on top of these logs and push them around to keep them from getting stuck. Suppose one such log is a solid cylinder of mass 800 kg, diameter 60 cm, and length 5.0 m. (a) What is the moment of inertia (a.k.a. rotational inertia) of the log? (b) A person standing on the log needs to keep its angular acceleration below about 0.25 rad/s2 so that he doesn’t fall off. What maximum (tangential) frictional force can he apply to the outside of the log? Assume any friction between the log and the water is negligible.

Solution

(a) Moment of Inertia of a cylinerical log about its axis = MR²/2 = [800x(60/200)²] / 2 = 72 kg m²

(b) Maximum tangential force applied by lumberjack so that angular acclearion does not reach 0.25 rad/s²

(Tangential Force)x(radius) = (Moment of inertia)x(angular accleration)

   Tangential Force = (72x0.25)/(0.3) = 60 N