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AP Physics C: Mechanics
6.5 Rolling
AdvancedMCQConceptual22.3k
A Cartesian coordinate graph with a horizontal time axis labeled t and a vertical angular velocity axis labeled \omega. The horizontal axis has three tick marks with text labels: 0 at the origin, t_1 at the midpoint, and 2t_1 at the right end. The vertical axis has three tick marks with text labels: -\omega_0 below the horizontal axis, 0 at the origin, and \omega_0 above the horizontal axis. A single solid straight line segment of uniform thickness starts at coordinates (0, \omega_0), extends downward with a constant negative slope, intersects the horizontal axis precisely at (t_1, 0), and ends at coordinates (2t_1, -\omega_0). The graph has bare axes with no gridlines. No other labels, lines, text, or axes appear.
Angular velocity \(\omega\) as a function of time \(t\) for the rolling cylinder.
A uniform solid cylinder of mass \(M\) and radius \(R\) is launched up an incline of angle \(\theta\) and rolls without slipping, momentarily stops at time \(t_1\), and rolls back down to its launch position at time \(2t_1\). The positive rotational direction is defined such that the cylinder has a positive angular velocity (\(\omega > 0\)) during its ascent, as shown in the graph of angular velocity \(\omega\) versus time \(t\). Which of the following statements correctly relates the features of the graph to the static friction force exerted on the cylinder by the incline?

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