Question

problem reference 8 - 3
a wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s². the wheel completes two revolutions.
what is the angular velocity of the wheel at the instant when it completes its second revolution?
75.4 rad/s
3.46 rad/s
0 rad/s
8.68 rad/s

Explanation:

Step1: Convert revolutions to radians

Two revolutions = $2 \times 2\pi = 4\pi$ rad ≈ 12.566 rad

Step2: Use rotational kinematic formula

Formula: $\omega^2 = \omega_0^2 + 2\alpha\theta$ (initial angular velocity $\omega_0=0$)
$\omega = \sqrt{2\alpha\theta} = \sqrt{2 \times 3.00 \times 12.566}$

Step3: Calculate angular velocity

$\omega = \sqrt{75.396} ≈ 8.68$ rad/s

Answer:

8.68 rad/s