Can we change the rotation speed of Earth if all cars, planes, ships, etc travel towards east or west together? I know when cars drive, there is action and reaction pair on the wheel, then is it possible to speed up or slow down the rotation of Earth if all cars and other machines travel towards one direction together?
 A: Earth + machines is an isolated system so angular momentum is conserved
\begin{align}
I_{\text{Earth}}\omega_{\text{Earth}}^{\text{before}} &= I_{\text{Machine}}\omega_{\text{Machine}} + I_{\text{Earth}}\omega_{\text{Earth}}^{\text{after}}\\
\Rightarrow
&\frac{\omega_{\text{Earth}}^{\text{after}}}{\omega_{\text{Earth}}^{\text{before}}} =1 - \frac{I_{\text{Machine}}\omega_{\text{Machine}}}{I_{\text{Earth}}\omega_{\text{Earth}}^{\text{before}}}  
\end{align}
Therefore the percent change in earths angular rotation speed is
\begin{align}
\frac{\omega^{\text{after}}_{\text{earth}}}{\omega^{\text{before}}_{\text{earth}}}=\frac{I_{\text{Machine}}\omega_{\text{Machine}}}{I_{\text{Earth}}\omega_{\text{Earth}}^{\text{before}}} &=\frac{5}{2}\frac{M_{\text{Machine}}}{M_{\text{Earth}}} \frac{v_{\text{Machine}}}{R\omega_{\text{Earth}}^{\text{after}}} \approx \left(10^{-27} \text{sec}/ \text{kg}\cdot\text{m}\right) \times p_{\text{Machine}}
\end{align}
In other words assuming all machines are moving at the equator, their momentum must be of the order of $10^{27}\text{kg}\cdot\text{m}/\text{sec}$ to get a $1\%$ change in earths angular speed, i.e. to increase/decrease the day by around a quarter of an hour.
In comparison notice that if all the cars on earth where to move at a very illegal speed, their combined momentum wont exceed $10^{14}\text{kg}\cdot\text{m}/\text{sec}$ which could only change the length of the day by less than $10$ nano seconds...
