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AP Physics C: Mechanics
5.1 Rotational Kinematics
IntermediateMCQMathematical16.8k
A Cartesian coordinate graph showing a horizontal axis labeled t (s) marked with major tick marks at 0, 1, 2, 3, and 4, and a vertical axis labeled \omega (rad/s) marked with major tick marks at 0, 6, 12, 18, and 24. Light gray gridlines form a uniform square grid across the plot area from t = 0 to 4 and \omega = 0 to 24. A thick solid black curve starts at the origin (0, 0), curves upward with increasing slope, passes through the points (2, 6) and (4, 24), and terminates at (4, 24). A straight dashed black line is tangent to the curve at the point (2, 6); this dashed line extends from (1, 0) on the horizontal axis through (2, 6) to (3, 12). A solid black dot marks the point of tangency at (2, 6). No other labels, curves, lines, text, or background shading appear.
Angular velocity versus time for a rotating disk with a tangent line at t = 2.0 s.
A disk rotates about a fixed axis perpendicular to its center. The disk's angular velocity \(\omega\) as a function of time \(t\) is shown in the graph and modeled by \(\omega(t) = ct^2\), where \(c\) is a positive constant. At \(t = 4.0\text{ s}\), the angular velocity is \(24\text{ rad/s}\), and a dashed line tangent to the curve at \(t = 2.0\text{ s}\) has a slope of \(6.0\text{ rad/s}^2\). What is the total angular displacement of the disk between \(t = 0\text{ s}\) and \(t = 4.0\text{ s}\)?

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