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A physical pendulum has length L=1.45m and mass m=2.00 kg is attached to a frictionless pivot as shown. The pendulum has non-constant density where the upper end is four times denser than the bottom end, i.e. Atop=41pottom. The pivot is located a distance h= 0.5 L m below the upper end of the pendulum. The pendulum is lifted an angle of 0=38.4°and released from rest. pivot

A physical pendulum has length L=1.45m and mass m=2.00 kg is attached to a frictionless pivot as shown. The pendulum has non-constant density where the upper end is four times denser than the bottom end, i.e. Atop=41pottom. The pivot is located a distance h= 0.5 L m below the upper end of the pendulum. The pendulum is lifted an angle of 0=38.4°and released from rest. pivot

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A physical pendulum has length \( L = 1.45 \, \text{m} \) and mass \( m = 2.00 \, \text{kg} \) is attached to a frictionless pivot as shown. The pendulum has non-constant density where the upper end is four times denser than the bottom end, i.e. \( \lambda_{\text{top}} = 4 \lambda_{\text{bottom}} \). The pivot is located a distance \( h = 0.5 \, L \, \text{m} \) below the upper end of the pendulum. The pendulum is lifted an angle of \( \theta = 38.4^\circ \) and released from rest. ### Diagram Description The diagram shows a pendulum hanging from a horizontal bar, labeled as a "pivot." The pendulum is a rod pivoted at a point \( h \), which is \( 0.5L \) below the top. The pendulum is shown at an angle \( \theta \) from the vertical. ### Questions a) What is the translational velocity of the bottom tip of the pendulum at the moment that gravitational potential energy is 50% of its maximum? b) What effect would doubling the mass and length of the physical pendulum have on the answer to part (a) of the problem? c) Draw graphs of angular acceleration, tangential translational acceleration, and centripetal acceleration as functions of the instantaneous angle that the pendulum makes with the vertical. In all three graphs, show the behavior of the acceleration from release with \( \theta = 38.4^\circ \) until the pendulum is vertical and \( \theta = 0 \).
Transcribed Image Text:A physical pendulum has length \( L = 1.45 \, \text{m} \) and mass \( m = 2.00 \, \text{kg} \) is attached to a frictionless pivot as shown. The pendulum has non-constant density where the upper end is four times denser than the bottom end, i.e. \( \lambda_{\text{top}} = 4 \lambda_{\text{bottom}} \). The pivot is located a distance \( h = 0.5 \, L \, \text{m} \) below the upper end of the pendulum. The pendulum is lifted an angle of \( \theta = 38.4^\circ \) and released from rest. ### Diagram Description The diagram shows a pendulum hanging from a horizontal bar, labeled as a "pivot." The pendulum is a rod pivoted at a point \( h \), which is \( 0.5L \) below the top. The pendulum is shown at an angle \( \theta \) from the vertical. ### Questions a) What is the translational velocity of the bottom tip of the pendulum at the moment that gravitational potential energy is 50% of its maximum? b) What effect would doubling the mass and length of the physical pendulum have on the answer to part (a) of the problem? c) Draw graphs of angular acceleration, tangential translational acceleration, and centripetal acceleration as functions of the instantaneous angle that the pendulum makes with the vertical. In all three graphs, show the behavior of the acceleration from release with \( \theta = 38.4^\circ \) until the pendulum is vertical and \( \theta = 0 \).
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