Question

question 5
the earth takes slightly less than one day to complete one rotation about the axis passing through its poles. the actual time is 8.616×10⁴ s. given this information, what is the angular speed of the earth about its axis?
○ 7.292×10⁻⁵ rad/s
○ 2.321×10⁻⁶ rad/s
○ 6.334×10⁻⁴ rad/s
○ 1.990×10⁻⁷ rad/s
○ 9.951×10⁻⁵ rad/s

Explanation:

Step1: Recall the formula for angular speed

The formula for angular speed \(\omega=\frac{\Delta\theta}{\Delta t}\). For one full rotation, \(\Delta\theta = 2\pi\) radians.

Step2: Substitute the values into the formula

We know that \(\Delta t=8.616\times 10^{4}\text{ s}\) and \(\Delta\theta = 2\pi\). So \(\omega=\frac{2\pi}{8.616\times 10^{4}}\).
Calculate \(\frac{2\times3.1416}{8.616\times 10^{4}}=\frac{6.2832}{8.616\times 10^{4}}\).
\(6.2832\div8.616 = 0.7292\), and \(\frac{0.7292}{10^{4}}=7.292\times 10^{-5}\text{ rad/s}\)

Answer:

\(7.292\times 10^{-5}\text{ rad/s}\) (the first option)