Question

test information
description: show all you work, including units, on separate paper. follow the \problem solving method\. this final exam is cumulative and covers material from the entire course.
instructions: from the list of choices, select the one best answer.
multiple attempts: not allowed. this test can only be taken once.
force completion: this test can be saved and resumed later. your answers are saved automatically.
question completion status: question numbers grid
question 44 of 62
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question 44
the angular speed of a flywheel increases from 40 rad/s to 125 rad/s in a time of 4.00 s. what is the angle through which the flywheel turns?
options: 660 rad, 170 rad, 165 rad, 330 rad

Explanation:

Step1: Identify the motion type

The flywheel undergoes angular motion with constant angular acceleration (since angular speed increases uniformly). We use the formula for angular displacement in uniformly accelerated angular motion: $\theta=\frac{\omega_i + \omega_f}{2}\times t$, where $\omega_i$ is initial angular speed, $\omega_f$ is final angular speed, and $t$ is time.

Step2: Substitute values

Given $\omega_i = 40\ \text{rad/s}$, $\omega_f = 125\ \text{rad/s}$, $t = 4.00\ \text{s}$. Substitute into the formula: $\theta=\frac{40 + 125}{2}\times4$.

Step3: Calculate

First, $\frac{40 + 125}{2}=\frac{165}{2}=82.5$. Then, $82.5\times4 = 330\ \text{rad}$.

Answer:

330 rad