Answer:
The automobile tire rotates 91 revolutions
Explanation:
Given;
angular acceleration of the automobile, α = 2.13 rad/s²
time interval, t = 23.2-s
To calculate the number of revolutions, we apply the first kinematic equation;
[tex]\theta = \omega_i \ + \frac{1}{2} \alpha t^2[/tex]
the initial angular velocity is zero,
[tex]\theta =0\ + \frac{1}{2} (2.13) (23.2)^2\\\\\theta = 573.2256 \ Rad[/tex]
Find how many revolutions that are in 573.2256 Rad
[tex]N = \frac{\theta}{2 \pi} = \frac{573.2256}{2\pi} \\\\N = 91 \ revolutions[/tex]
Therefore, the automobile tire rotates 91 revolutions
