Question

A wheel rotating with a constant angular acceleration turns through 22 revolutions during a 5 s time interval. Its angular velocity at the end of this interval is 12 rad/s. What is the angular acceleration of the wheel? Note that the initial angular velocity is not zero. Answer in units of rad/s 2 .

Answer 1

Answer:

0.52rad/s^2

Explanation:

To find the angular acceleration you use the following formula:

$\omega^2=\omega_o^2+2\alpha\theta$   (1)

w: final angular velocity

wo: initial angular velocity

θ: revolutions

α: angular acceleration

you replace the values of the parameters in (1) and calculate α:

$\alpha=\frac{\omega^2-\omega_o^2}{2\theta}$

you use that θ=22 rev = 22(2π) = 44π

$\alpha=\frac{(12rad/s)^2-(0rad/s)^2}{2(44\pi)}=0.52\frac{rad}{s^2}$

hence, the angular acceñeration is 0.52rad/s^2