A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 64 cm and is wrapped around the top at a place where its radius is 2.2 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of +11 rad/s². What is the final angular velocity of the top when the string is completely unwound? Before string is pulled After string is pulled 00 1

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Chapter1: Units, Trigonometry. And Vectors
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**Title: Understanding the Physics of Spinning Tops**

**Introduction:**
A top is a classic toy designed to spin on its pointed end by pulling a string wrapped around its body. This example explores the physics behind how a top spins using angular acceleration.

**Problem Statement:**
A string with a length of 64 cm is wrapped around a top at a point where its radius measures 2.2 cm. The string's thickness is negligible. Initially, the top is at rest. As the free end of the string is pulled, it unwinds, providing the top with an angular acceleration of +11 rad/s². Determine the final angular velocity of the top when the string is completely unwound.

**Diagrams:**

1. **Before String is Pulled:**
   - The top is shown with a string wound around it. The point where the string is wrapped represents the radius (r) of 2.2 cm.

2. **After String is Pulled:**
   - The top is depicted without the string around it, indicating the string has been completely unwound.
   - An arrow is labeled with angular velocity (ω), representing the direction of spin.
   - Another arrow (s) represents the displacement of the string as it is pulled.

**Conclusion:**
This problem illustrates the principles of angular motion and how force applied via a string can produce rotational movement. By calculating the angular velocity, we gain insights into how stored energy in the form of tension in the string gets transferred to rotational kinetic energy in the top.
Transcribed Image Text:**Title: Understanding the Physics of Spinning Tops** **Introduction:** A top is a classic toy designed to spin on its pointed end by pulling a string wrapped around its body. This example explores the physics behind how a top spins using angular acceleration. **Problem Statement:** A string with a length of 64 cm is wrapped around a top at a point where its radius measures 2.2 cm. The string's thickness is negligible. Initially, the top is at rest. As the free end of the string is pulled, it unwinds, providing the top with an angular acceleration of +11 rad/s². Determine the final angular velocity of the top when the string is completely unwound. **Diagrams:** 1. **Before String is Pulled:** - The top is shown with a string wound around it. The point where the string is wrapped represents the radius (r) of 2.2 cm. 2. **After String is Pulled:** - The top is depicted without the string around it, indicating the string has been completely unwound. - An arrow is labeled with angular velocity (ω), representing the direction of spin. - Another arrow (s) represents the displacement of the string as it is pulled. **Conclusion:** This problem illustrates the principles of angular motion and how force applied via a string can produce rotational movement. By calculating the angular velocity, we gain insights into how stored energy in the form of tension in the string gets transferred to rotational kinetic energy in the top.
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