### Example Problem: Dynamics of a Rotating Disk**Problem 10.10:**A uniform disk with a mass of 40.0 kg and a radius of 0.200 m is pivoted at its center about a horizontal, frictionless axle that remains stationary. The disk is initially at rest, and then a constant force \( F = 30.0 \, \text{N} \) is applied tangent to the rim of the disk. 1. **(a)** What is the magnitude \( v \) of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.200 revolutions?2. **(b)** What is the magnitude \( a \) of the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.200 revolutions?### Detailed Explanation:**Part (a): Calculating the Tangential Velocity**- **Given Data:** - Mass of the disk (\( m \)) = 40.0 kg - Radius of the disk (\( R \)) = 0.200 m - Applied force (\( F \)) = 30.0 N - Revolutions (\( \theta \)) = 0.200 revolutions- **Step-by-Step Solution:** 1. **Convert revolutions to radians:** \[ \theta = 0.200 \, \text{revolutions} \times 2\pi \, \text{radians/revolution} = 0.4\pi \, \text{radians} \] 2. **Torque Calculation:** The torque (τ) due to the force applied tangent to the rim is: \[ \tau = F \times R = 30.0 \, \text{N} \times 0.200 \, \text{m} = 6.0 \, \text{Nm} \] 3. **Moment of Inertia of the Disk:** For a uniform disk, the moment of inertia (I) about its center is: \[ I = \frac{1}{2} m R^2 = \frac{1}{2} \times 40.0 \, \text{kg} \times (0.200 \, \text

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10.10 .. A uniform disk with mass 40.0 kg and radius 0.200 m Is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force F 30.0 N is applied tangent to the rim of the disk. (a) What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.200 revolution? (b) What s the magnitude a of the resultant acceleration of a point on the im of the disk after the disk has turned through 0.200 revolution?

10.10 .. A uniform disk with mass 40.0 kg and radius 0.200 m Is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force F 30.0 N is applied tangent to the rim of the disk. (a) What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.200 revolution? (b) What s the magnitude a of the resultant acceleration of a point on the im of the disk after the disk has turned through 0.200 revolution?

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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