**Transcription and Explanation for Educational Use:****Text:**A metal rod with a mass of 2.30 kg has one end resting on the floor. The other end is lifted up with a vertical rope, raising the rod to an angle of 30° above the horizontal. Find the amount of force needed to hold the rod in that position. (The weight of the rod is concentrated at its center of gravity. The length is not needed.)**Diagram Description:**The diagram shows a metal rod positioned at a 30° angle above the horizontal surface. One end of the rod rests on the floor while the other end is elevated using a vertical rope. The rope is depicted as being held by a hand, with a force labeled as "F" directed upwards, opposing the gravitational force acting on the rod. The center of gravity, where the weight is concentrated, is implied to be at the midpoint of the rod, balancing the system in equilibrium. The setup illustrates the mechanical balance required to maintain the rod at a specified angle, focusing on the vertical force needed to counteract gravity and stabilize the rod in its raised position without requiring knowledge of the rod's length. **FORMULAS**- $ s = r\theta $, $ v = r\omega $, $ a = r\alpha $ - **Torque:** $ \tau = F(\sin\theta)r $ - $ \tau = Fl $, where $ l = $ lever arm**Equilibrium:** $ \sum \tau = 0 $**Non-equilibrium:** $ \sum \tau = I\alpha $**Moments of Inertia for Various Rigid Objects of Uniform Composition:****Point Mass:** $ I = MR^2 $**Diagrams and Explanations:**The image contains illustrations and moments of inertia for various rigid objects:1. **Hoop or Thin Cylindrical Shell:** - Moment of Inertia: $ I = MR^2 $ - Illustration: A circular hoop with radius $ R $.2. **Solid Sphere:** - Moment of Inertia: $ I = \frac{2}{5} MR^2 $ - Illustration: A solid sphere with radius $ R $.3. **Solid Cylinder or Disk:** - Moment of Inertia: $ I = \frac{1}{2} MR^2 $ - Illustration: A solid cylinder with radius $ R $.4. **Thin Spherical Shell:** - Moment of Inertia: $ I = \frac{2}{3} MR^2 $ - Illustration: A hollow sphere with radius $ R $.5. **Long, Thin Rod with Rotation Axis Through Center:** - Moment of Inertia: $ I = \frac{1}{12} ML^2 $ - Illustration: A long rod rotating around its center with length $ L $.6. **Long, Thin Rod with Rotation Axis Through End:** - Moment of Inertia: $ I = \frac{1}{3} ML^2 $ - Illustration: A long rod rotating around an axis at one end with length $ L $.---These formulas and diagrams illustrate the rotational motion and the moments of inertia for various shapes, each representing common scenarios in physics and engineering. The illustrations show the geometric shape and the axis of rotation.

Torque is the turning ability of a force .It is given as the product of force with perpendicular…

A metal rod with a mass of 2.30 kg has one end resting on the floor. The other end is lifted up with a vertical rope, raising the rod to an angle of 30° above the horizontal. Find the amount of force needed to hold the rod in that position. (The weight of the rod is concentrated at its center of gravity. The length is not needed.) F 30°

A metal rod with a mass of 2.30 kg has one end resting on the floor. The other end is lifted up with a vertical rope, raising the rod to an angle of 30° above the horizontal. Find the amount of force needed to hold the rod in that position. (The weight of the rod is concentrated at its center of gravity. The length is not needed.) F 30°

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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