Review Sign Conventions  
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It is helpful to establish a consistent sign convention for internal torque, twist angle, and angle of rotation.

The figure shows a cylinder on an x y coordinate system. The X axis passes through the center of the cylinder. The positive twist angle phi acts on the outer surface of the cylinder and is in an counterclockwise direction.

• A positive internal torque acts in a right-hand-rule sense about the outer normal to a cross section.

• A positive twist angle in a shaft segment acts in a right-hand-rule sense about the outer normal to a cross section.

• A positive angle of rotation is a rotation of the cross section in a right-hand-rule sense about the positive x-axis defined for the shaft.