AP Physics C Mechanics 2.10: Circular Motion

Relate circular motion to tangential speed, radius, centripetal acceleration, and the inward net force acting on the moving object.

[Maximum number: 1]

A wind turbine includes a three-blade system that rotates about an axis through the end of each blade, as shown in Figure 1. Each blade has a length L and mass M, with a center of mass located at a distance $\frac{L}{3}$ from the axis of rotation, as shown in Figure 2.

While the wind blows, the three-blade system operates at a constant angular speed $\omega_{0}=2.6 \mathrm{rad} / \mathrm{s}$ . The length of one blade is $L=36 \mathrm{~m}$ . The numerical value of the rotational inertia of the system is $I_{\text {sys }}=6.7 \times 10^{6} \mathrm{~kg} \cdot \mathrm{~m}^{2}$ . Calculate the time T it takes the outer edge of a single blade to complete one revolution.

For calculating the correct answer with correct units (2.4 s)

1 point

Example Solution
$\begin{aligned} v=r \omega v=L \omega_{0} \frac{d}{t}=L \omega_{0} \end{aligned}$ $t=\frac{d}{L \omega_{0}}=\frac{2 \pi L}{L \omega_{0}}=\frac{2 \pi}{\omega_{0}}$ $t=\frac{2 \pi}{(2.6 \operatorname{rad} / \mathrm{s})}$ $\therefore t=2.4 \mathrm{~s}$

Total for part (b) 1 point

All question bank results loaded

2.10.A—Describe the motion of an object traveling in a circular path question 1