A wheel starting from rest has \alpha = 4\text{rad/s}^2. After how many full revolutions does its angular speed reach 20\text{rad/s}?

8.0 Apply \omega^2 = 2\alpha\theta with \omega0 = 0: \theta = \omega^2/(2\alpha) = 400/8 = 50\text{rad}. Convert to revolutions: 50/(2\pi) \approx 7.96 \approx 8.0 revolutions.

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Acemy

Rotational Kinematics

AP Physics 1· difficulty 3/5

\alpha = 4~\text{rad/s}^2

A
$5.0$
B
$4.0$
C
$2.5$
D
$8.0$
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Explanation

\omega^2 = 2\alpha\theta

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