AP Physics C: Mechanics 2.10 Circular Motion Questions

Analyse circular paths and orbits by combining radial and tangential acceleration, real-force components, contact constraints, curved-road dynamics, and Kepler relations.

Exam points

determine radial and tangential acceleration from a circular path and its changing speed
resolve real forces radially to analyse tension, normal force, friction, or gravity
analyse flat or banked circular curves and their friction or geometry limits
apply loss-of-contact boundaries in vertical loops and other constrained circular paths
combine radial dynamics with energy or kinematics to determine minimum starting conditions

Covered syllabus points

2.10.A—Describe the motion of an object traveling in a circular path 2.10.B—Describe circular orbits using Kepler’s third law

[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

[Maximum number: 1]

An Earth satellite in a circular orbit of radius R has a period T. What is the period of an Earth satellite in a circular orbit of radius 4 R ?

2 T

4 T

6 T

8 T

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Covered syllabus points

Question 1

Question 2