Show your work and include units with your answers for full credit. In the past,

Question

Show your work and include units with your answers for full credit.

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.

Explanation / Answer

Here ,

m = 800 Kg

radius ,r = 60/2 = 30 cm = 0.30 m

L = 5 m

a) for the log

moment of inertia of log = 0.5 * m * r^2

moment of inertia of log = 0.5 * 800 * 0.3^2

moment of inertia of log = 36 Kg.m^2

the moment of inertia of log is 36 Kg.m^2

part b)

angular acceleration , a = 0.25 rad/s^2

maximum tangential frictional force = a * m * r

maximum tangential frictional force = 0.25 * 60 * 0.30

maximum tangential frictional force = 4.5 N

the maximum tangential frictional force is 4.5 N

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