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 degree until the pendulum is vertical and theta =0 degree. The diagram illustrates a physical pendulum. It consists of a rigid rod attached to a pivot point above a horizontal support. Here's a detailed explanation of the components:1. **Pivot**: The upper end of the rod is connected to this fixed point, allowing the rod to swing freely back and forth.2. **Rod**: A straight, thick line representing the rigid body of the pendulum, which swings due to gravitational forces.3. **Height (h)**: The vertical distance from the pivot to the center of mass of the rod. This is indicated by a small line segment marked as 'h'.4. **Angle (θ)**: The angle between the rod and the vertical dashed line (representing the equilibrium position). The angle indicates the displacement of the pendulum from its resting position.5. **Arrow**: A small curved arrow at the bottom of the pendulum shows the direction of motion, which is typically periodic.This setup is used to study rotational motion and the factors affecting the period of oscillation for physical pendulums. A physical pendulum has a length \( L = 1.45 \, \text{m} \) and mass \( m = 2.00 \, \text{kg} \), and it is attached to a frictionless pivot as shown. The pendulum exhibits a non-uniform density, where the upper end is three times denser than the bottom end, i.e., \( \lambda_{\text{top}} = 4 \lambda_{\text{bottom}} \). The pivot is located a distance \( h = \frac{1}{12} L \, \text{m} \) below the upper end of the pendulum. The pendulum is lifted to an angle of \( \theta = 38.4^\circ \) and released from rest.In this description, there is no visual graph or diagram provided for further analysis.

Name: a. What is the translational velocity of the bottom tip of the pendulu
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Description: 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)

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Answered: a. What is the translational velocity…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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 degree until the pendulum is vertical and theta =0 degree.

The diagram illustrates a physical pendulum. It consists of a rigid rod attached to a pivot point above a horizontal support. Here's a detailed explanation of the components:

1. **Pivot**: The upper end of the rod is connected to this fixed point, allowing the rod to swing freely back and forth.

2. **Rod**: A straight, thick line representing the rigid body of the pendulum, which swings due to gravitational forces.

3. **Height (h)**: The vertical distance from the pivot to the center of mass of the rod. This is indicated by a small line segment marked as 'h'.

4. **Angle (θ)**: The angle between the rod and the vertical dashed line (representing the equilibrium position). The angle indicates the displacement of the pendulum from its resting position.

5. **Arrow**: A small curved arrow at the bottom of the pendulum shows the direction of motion, which is typically periodic.

This setup is used to study rotational motion and the factors affecting the period of oscillation for physical pendulums.

A physical pendulum has a length \( L = 1.45 \, \text{m} \) and mass \( m = 2.00 \, \text{kg} \), and it is attached to a frictionless pivot as shown. The pendulum exhibits a non-uniform density, where the upper end is three times denser than the bottom end, i.e., \( \lambda_{\text{top}} = 4 \lambda_{\text{bottom}} \). The pivot is located a distance \( h = \frac{1}{12} L \, \text{m} \) below the upper end of the pendulum. The pendulum is lifted to an angle of \( \theta = 38.4^\circ \) and released from rest.

In this description, there is no visual graph or diagram provided for further analysis.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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