A truck with 0.420-m-radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?
Solution:
The linear velocity, v and the angular velocity \omega are related by the equation
v=r\omega \ \text{or} \ \omega=\frac{v}{r}From the given problem, we are given the following values: r=0.420 \ \text{m} and v=32.0 \ \text{m/s}. Substituting these values into the formula, we can directly solve for the angular velocity.
\begin{align*}
\omega & = \frac{v}{r} \\ \\
\omega & = \frac{32.0 \ \text{m/s}}{0.420 \ \text{m}} \\ \\
\omega & = 76.1905 \ \text{rad/s} \\ \\
\omega & = 76.2 \ \text{rad/s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}
Then, we can convert this into units of revolutions per minute:
\begin{align*}
\omega & = 76.1905 \ \frac{\bcancel{\text{rad}}}{\bcancel{\text{sec}}}\times \frac{1 \ \text{rev}}{2\pi\ \bcancel{\text{rad}}}\times \frac{60\ \bcancel{\text{sec}}}{1\ \text{min}} \\ \\
\omega & = 727.5657\ \text{rev/min} \\ \\
\omega & = 728\ \text{rev/min} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}
Advertisements
Advertisements