Angle of rotation problems can come up in several NCEES FE Exams: Civil, Mechanical, and Other Disciplines. In mathematics, the angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle.

A clockwise rotation is considered a negative rotation, so that, for instance, a rotation of 310 degrees (counter clockwise) can also be called a rotation of negative 50° (since 310 degrees + 50 degrees = 360 degrees, a full rotation ( or turn)).

A counter clockwise rotation of more than one complete turn is normally measured modjulo 360 degrees, meaning that 360 degrees is subtracted off as many times as possible to leave a non-negative measurement less than 360 degrees.

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### So Here’s the Problem:

### Find the Explanation Given Below:

**Refer to the Mohr’s Circle section in the Mechanics of Materials chapter of the FE Reference Handbook.**

Ultimately, we must determine the angle rotation needed to get the stress element to a principal stress state.

### Steps To Determine the Angle of Rotation Needed:

- Draw a quick Mohr’s circle based on what’s shown in the stress element.
- Draw a right triangle from the center of the Mohr’s circle to a known point along the circle. Determine the Mohr’s circle’s angle between the known point and the sigma axis (x-axis), which is where the principal stress occurs. That will be the Mohr’s circle rotation angle needed to get to a principal stress state.
- Convert the Mohr’s circle’s rotation angle needed to get to a principal stress state to the stress element’s angle needed to get to a principal stress state.

**The correct answer is D.**

I hope you found this week’s video helpful. In upcoming videos, I will share some more studying strategies and also cover some more problems including engineering economics practice problems.

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I’ll see you next week.

Anthony Fasano, P.E.

Engineering Management Institute

*Author of Engineer Your Own Success*

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