Angular Velocity and Radian Measurement in Physics Problems

By Consumer Dummies

In physics, you can combine angular velocity with radian measurement to calculate the distance and speed of a moving object. For example, you can calculate the angular speed of a car as it travels along a curve.

Here are some practice questions that you can try.

Practice questions

  1. The moon rotates once on its axis in about 27 days. If the moon’s radius is 1,734 kilometers, how far in kilometers does an astronaut standing on the moon’s surface move in 1 day?

  2. You drive along the freeway at 60 miles per hour. You go through a curve with a radius of one quarter mile. What is your angular speed in radians per hour in this curve?

Answers

The following are the answers to the practice questions:

  1. image0.png

    The angular speed of the moon is

    image1.png

    For this problem,

    image2.png

    (one complete revolution) and

    image3.png

    so the angular speed is

    image4.png

    To find the angle through which the astronaut rotates in one day, solve the equation above for

    image5.png

    (the subscript ast means that this is the angle through which the astronaut rotates in one day, not the angle through which the moon rotates in 27 days). The result is

    image6.png

    where

    image7.png

    is the time during which the astronaut rotates. Insert the known quantities to find

    image8.png

    To find the distance that the astronaut travels, use the equation relating arc length to arc radius and the angle subtended by the arc:

    image9.png

    Use r = 1,734 kilometers to find

    image10.png

  2. image11.png

    The angular speed is related to the tangential velocity and the radius of curvature by

    image12.png

    Solve this for

    image13.png

    and insert the known quantities of

    image14.png

    and

    image15.png

    The result is

    image16.png