Question 2.SP.28: A wheel 200 mm in diameter coasts to rest from a speed of 80......

Schaum’s Outline of Engineering Mechanics Dynamics [1352259]

A wheel 200 mm in diameter coasts to rest from a speed of 800 rpm in 600 s. Determine the angular acceleration.

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Given $\omega_{0}=800 \mathrm{rpm}=83.8 \mathrm{rad} / \mathrm{s}$ and $\omega=0$ at $t=600 \mathrm{~s}$ , then

$\alpha=\frac{\omega-\omega_{0}}{t}=\frac{-83.8 \mathrm{rad} / \mathrm{s}}{600 \mathrm{~s}}=\underline{-0.14 \mathrm{rad} / \mathrm{s}^{2}} \quad \text { (deceleration) }$

The acceleration is negative. This means that the angular velocity is in one direction, while the angular acceleration is oppositely directed, thereby indicating a slowing down of the wheel.

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