- $86500 \textrm{ s}$
- $7.27 \times 10^{-5}\textrm{ rad/s}$
- $470 \textrm{ m/s}$

### Solution video

# OpenStax College Physics, Chapter 6, Problem 4 (Problems & Exercises)

### Calculator Screenshots

*π*radians— that's 1 full day of rotation— divided by the time it takes to do that which is 86400 seconds. So the angular speed then is 7.27 times 10 to the minus 5 radians per second. The linear speed on a point at the equator on the surface of the Earth is going to be the radius of the Earth multiplied by this angular speed. So that's 6.4 times 10 to the 6 meters—radius— times 2

*π*radians over 86400 seconds which is 470 meters per second.

## Comments

For part C. Quick question, why would we not use 360 in the place of change of theta instead of 2 (π)? Thank you in advance.

Hi phillipmoreno,

Thank you for the question. Degrees are not considered **mks** units. **mks** refers to **m**eters, **k**ilograms, **s**econds, which are the units needed for formulas. Another way to look at it is that, since radians are the ratio of the distance traveled along the edge of a circle divided by the circle's radius, radians tell you how many radii have been traveled (the name radians could instead be expressed "number of radii". $2\pi$ radians is saying 6.28 radii in other words). When we divide the "number of radii" travelled by time, we get units of "radii per second", which then gets multiplied by "meters per radius", arriving at "meters per second". I'm putting strange units in quotes there, but I'm trying to help conceptualize the meaning of radians, and why they're helpful in formulas.

All the best,

Shaun