Angle-to-Radian Conversion in Physics Problems

By Consumer Dummies

In physics, it’s useful to know how to calculate angles in radians. But first, you need to convert those angles from degrees to radians. The following practice questions walk you through the conversion process.

Practice questions

  1. You cut a cake into 8 equal pieces. What is the angle, in radians, of the pointed end of each piece of cake?

  2. A drawbridge pivots upward from the horizontal position and moves through two-thirds of the angle between the horizontal and vertical positions. Through what angle (in radians) has the drawbridge moved?

  3. Cleaning up after a party, you find leftover pizza slices. The pizzas were round, and the slices were all cut through the center. You find two slices that together make a quarter of a pizza and three slices that are each an eighth of a pizza. If you put all the slices side by side as in a pizza, what is the total angle made (in radians)?

Answers

The following are the answers to the practice questions:

  1. 0.785 rad

    A full circle has an angle of

    image0.png

    To find the angle

    image1.png

    that is one eighth of this, you must divide

    image2.png

    by 8:

    image3.png

  2. image4.png

    The angle between horizontal and vertical is 90 degrees, or a quarter of a circle. Because there are

    image5.png

    in a circle, there are

    image6.png

    in 90 degrees. The angle

    image7.png

    through which the drawbridge moved is then two-thirds of

    image8.png

  3. 3.9 rad

    You’re told that the first two slices make a quarter of a whole pizza, which means that they make a quarter of a circle. There are

    image9.png

    in a circle, so this angle is

    image10.png

    The last three slices each make an eighth of a circle, so they each make an angle

    image11.png

    The total angle made when the slices are laid side by side is

    image12.png

    Using

    image13.png

    this gives

    image14.png