Video Transcript
An angular displacement of 666 degrees is equal to blank revolutions.
In this question, we’re dealing with two different ways to express angular displacement. Specifically, we need to convert a value given in degrees to revolutions. To do this, we should recall that one revolution refers to one full turn around a circle, which also measures 360 degrees. This equality is key to helping us make this conversion.
We’re starting with this measurement of 666 degrees, and we’re going to multiply it by this conversion factor. We’ve already established that one revolution equals 360 degrees. So, because the conversion factor’s numerator is equal to its denominator, we know that the conversion factor as a whole is just equal to one. Therefore, when we multiply 666 degrees by the conversion factor, we won’t be changing its value at all, just writing it in a different way.
Further, notice that we wrote this fraction with revolutions in the numerator and degrees in the denominator on purpose. This way, we can cancel degrees out of the expression entirely, leaving revolutions as the only angular unit associated with this quantity. Now, we can rewrite this as 666 divided by 360 revolutions. And finally calculating, this comes out to exactly 1.85 revolutions. We have our answer. So, filling in the blank, an angular displacement of 666 degrees is equal to 1.85 revolutions.
