### Understanding Circular Motion: Minimum Angular VelocityWhen swinging a ball of mass \( m \) in a vertical circle with a string of length \( L \), you need to maintain a minimum angular velocity \( \omega_{\text{min}} \) to ensure that the ball completes the full circle without the string going slack at the top.#### Part A**Objective:** Derive an expression for \( \omega_{\text{min}} \) in terms of the gravitational acceleration \( g \) and the string length \( L \).**Instructions:** Express your answer using the variables \( L \) and \( g \).\[ \omega_{\text{min}} = \]**Action:** Submit your answer once you've derived the expression.---#### Part B**Objective:** Calculate \( \omega_{\text{min}} \) in revolutions per minute (rpm) for a ball weighing 65 grams, tied to a string 1.0 meter in length.**Instructions:**Express your calculation in rpm.\[ \omega_{\text{min}} = \]**Action:** Submit your calculation to verify the result.---Explore these concepts to deepen your understanding of the dynamics of circular motion, and ensure your calculations are submitted for confirmation.

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Suppose you swing a ball of mass m in a vertical circle on a string of length L. As you probably know from experience, there is a minimum angular velocity wmin you must maintain if you want the ball to complete the full circle without the string going slack at the top. Find an expression for wmin in terms of g and L. Express your answer in terms of the variable L and the free-fall acceleration g. Wmin = Submit Part B Wmin = 195| ΑΣΦ Submit Request Answer Evaluate wmin in rpm for a 65 g ball tied to a 1.0-m-long string. Express your answer in revolutions per minute. 15. ΑΣΦ ? Request Answer ? rpm

Suppose you swing a ball of mass m in a vertical circle on a string of length L. As you probably know from experience, there is a minimum angular velocity wmin you must maintain if you want the ball to complete the full circle without the string going slack at the top. Find an expression for wmin in terms of g and L. Express your answer in terms of the variable L and the free-fall acceleration g. Wmin = Submit Part B Wmin = 195| ΑΣΦ Submit Request Answer Evaluate wmin in rpm for a 65 g ball tied to a 1.0-m-long string. Express your answer in revolutions per minute. 15. ΑΣΦ ? Request Answer ? rpm

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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