Video Transcript
Complete the following sentence. An angular displacement of blank radians is equal to an angular displacement of 155 degrees. Give your answer to two decimal places.
We’re talking here about angular displacement. So, we can imagine an object moving through a circular arc. And we’re told this object moves through an angular displacement of 155 degrees, or slightly less than one-half of a revolution around the circle. We want to know how many radians this is equivalent to. We can note that if we were to go all the way around this circular arc in one complete revolution, that would be equal to 360 degrees or, in units of radians, two 𝜋 radians.
Since 360 degrees is equal to two 𝜋 radians, that means that two 𝜋 radians divided by 360 degrees equals one. Therefore, if we multiply some number by this fraction, two 𝜋 radians divided by 360 degrees, we won’t change that number since we’re effectively multiplying by one. But notice what happens if we take our angular displacement in degrees and we multiply it by this fraction that we just saw is equal to one. When we do this, the units of degrees in numerator and denominator cancel out. And we’ll be left with a result when we multiply through in radians.
Multiplying 155 by two 𝜋 and dividing that by 360, we find a result of 2.70526 and so on radians. We’re to round our answer to two decimal places. When we do this, we find a result of 2.71 radians. So then, an angular displacement of 2.71 radians is equal to an angular displacement of 155 degrees.
