AP Physics C: Mechanics 2.10 A Describe the Motion of an Object Traveling in a Circular Path Questions

Describe circular motion through radial and tangential acceleration, centripetal force requirements, constrained contact, curved roads, vertical loops, and parametric models.

Exam points

determine radial acceleration magnitude and its inward direction from speed and radius
sum real force components in the radial direction instead of adding a separate centripetal force
use parametric position functions to identify circular radius, speed, and acceleration
include tangential acceleration when speed changes while radial acceleration remains inward
determine the friction-limited speed of a vehicle on a flat circular curve

[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

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AP Physics C: Mechanics 2.10 A Describe the Motion of an Object Traveling in a Circular Path Questions question 1