A jewel smith wishing to buff a finished piece of jewelry attaches a buffing disk to his drill. The radius of the disk is 2.30 mm, and he operates it at 2.30 x 10° rad/s. (a) Determine the tangential speed, in m/s, of the rim of the disk. m/s (b) The jeweler increases the operating speed so that the tangential speed of the rim of the disk is now 285 m/s. What is the period of rotation, in seconds, of the disk now?

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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**Educational Content: Determining Tangential Speed and Period of Rotation**

A jeweler, aiming to buff a finished piece of jewelry, attaches a buffing disk to a drill. The following problem explores the physics of this process, specifically focusing on angular velocity and tangential speed.

**Given:**
- Radius of the disk: \(2.30 \, \text{mm}\)
- Angular velocity: \(2.30 \times 10^4 \, \text{rad/s}\)

**Task (a):** Determine the tangential speed, in meters per second (m/s), of the rim of the disk.
- Answer Box: [____] m/s

**Task (b):** The jeweler increases the operating speed so that the tangential speed of the rim of the disk is now 285 m/s. What is the period of rotation, in seconds, of the disk now?
- Answer Box: [____] s

This exercise engages with basic principles of rotational motion, employing formulas such as:

\[ v = \omega \times r \]

Where \( v \) is the tangential speed, \( \omega \) the angular velocity, and \( r \) the radius of the disk.

For Task (b), the formula for the period \( T \) of rotation, which is the inverse of frequency \( f \), is used:

\[ T = \frac{2\pi}{\omega} \]

Understanding these principles is crucial for students studying rotational dynamics in physics.
Transcribed Image Text:**Educational Content: Determining Tangential Speed and Period of Rotation** A jeweler, aiming to buff a finished piece of jewelry, attaches a buffing disk to a drill. The following problem explores the physics of this process, specifically focusing on angular velocity and tangential speed. **Given:** - Radius of the disk: \(2.30 \, \text{mm}\) - Angular velocity: \(2.30 \times 10^4 \, \text{rad/s}\) **Task (a):** Determine the tangential speed, in meters per second (m/s), of the rim of the disk. - Answer Box: [____] m/s **Task (b):** The jeweler increases the operating speed so that the tangential speed of the rim of the disk is now 285 m/s. What is the period of rotation, in seconds, of the disk now? - Answer Box: [____] s This exercise engages with basic principles of rotational motion, employing formulas such as: \[ v = \omega \times r \] Where \( v \) is the tangential speed, \( \omega \) the angular velocity, and \( r \) the radius of the disk. For Task (b), the formula for the period \( T \) of rotation, which is the inverse of frequency \( f \), is used: \[ T = \frac{2\pi}{\omega} \] Understanding these principles is crucial for students studying rotational dynamics in physics.
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