Gravitational torque on an outstretched arm

Your arm has a mass of 3.0 kg, and its center of mass is 30 cm from your shoulder. What is the gravitational torque on your arm when it is stretched out horizontally to one side, taking the shoulder to be the axis?

The total gravitational force acting on your arm is

|F| = (3.0 kg)(9.8 m/s²) = 29 N .

For the purpose of calculating the gravitational torque, we can treat the force as if it acted at the arm's center of mass. The force is straight down, which is perpendicular to the line connecting the shoulder to the center of mass, so

F = |F| = 29 N .

Continuing to pretend that the force acts at the center of the arm, r equals 30 cm = 0.30 m, so the torque is

τ = rF = 9 N·m .