**Physics Problem: Rotational Motion of a Uniform Disk****Problem Statement:**A uniform disk with mass \(38.2 \, \text{kg}\) and radius \(0.240 \, \text{m}\) is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force of \(33.0 \, \text{N}\) is applied tangent to the rim of the disk.**Questions:**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 \(0.330\) revolution?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 \(0.330\) revolution?**Explanation:**This problem involves understanding concepts related to rotational motion, particularly angular velocity, tangential velocity, and the relationship between these velocities and acceleration when a force is applied to a rotating object.1. **Given Data:** - Mass of the disk, \(m = 38.2 \, \text{kg}\) - Radius of the disk, \(r = 0.240 \, \text{m}\) - Applied force, \(F = 33.0 \, \text{N}\) - Angular displacement, \(\theta = 0.330\) revolutions2. **Relevant Equations:** - Torque, \(\tau = r \times F\) - Moment of inertia of the disk, \(I = \frac{1}{2} m r^2\) - Angular acceleration, \(\alpha = \frac{\tau}{I}\) - Angular displacement in radians, \(\theta = 0.330 \times 2\pi\) - Kinematic equation for angular velocity, \(\omega^2 = \omega_0^2 + 2\alpha\theta\) - Tangential velocity, \(v = r\omega\) - Resultant acceleration, \(a = \sqrt{a_t^2 + a_c^2}\) - Tangential acceleration, \(a_t = r\alpha\) - Centripetal acceleration, \(a_c = r\omega^2\)**Step-by-Step Solution

Answered: Image /qna-images/answer/a297430f-7cda-48b5-a0fe-91b388c8b970.jpg

Q2) A uniform disk with mass 38.2 kg and radius 0.240 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 33.0 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 0.330 revolution? 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 0.330 revolution?

Q2) A uniform disk with mass 38.2 kg and radius 0.240 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 33.0 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 0.330 revolution? 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 0.330 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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