**Problem Statement:**The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.23 rad/s². It accelerates for 31.9 seconds, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 65.5 seconds after it begins rotating.**Solution Approach:**1. **Calculate Angular Displacement During Acceleration Phase:** - Use the formula for angular displacement during uniform acceleration: \[ \theta_1 = \omega_0 t + \frac{1}{2} \alpha t^2 \] - Where \(\omega_0 = 0\) (initial angular velocity), \(\alpha = 1.23 \, \text{rad/s}^2\), and \(t = 31.9 \, \text{s}\).2. **Calculate Angular Velocity at the End of Acceleration Phase:** - Angular velocity (\(\omega\)) can be calculated using: \[ \omega = \omega_0 + \alpha t \]3. **Calculate Angular Displacement During Constant Velocity Phase:** - After 31.9 seconds, the wheel travels with constant angular velocity for \(65.5 - 31.9 = 33.6 \, \text{s}\). - Angular displacement during this phase (\(\theta_2\)): \[ \theta_2 = \omega \times 33.6 \, \text{s} \]4. **Calculate Total Angular Displacement:** - Total angle \(\theta\) is the sum of \(\theta_1\) and \(\theta_2\): \[ \theta = \theta_1 + \theta_2 \]**Visual Aid:**- No graphs or diagrams are present in the original problem statement. A detailed step-by-step explanation accompanies the problem for clarity.

Given data: Initial angular velocity (ω0) = 0 rad/s Constant angular acceleration (α) = 1.23 rad/s2…

The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.23 rad/s². It accelerates for 31.9 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 65.5 s after it begins rotating.

The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.23 rad/s². It accelerates for 31.9 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 65.5 s after it begins rotating.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section10.4: Rotational Kinetic Energy

Problem 10.4QQ

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