Question

A 0.3-m-radius automobile tire rotates how many revolutions after starting from rest and accelerating at a constant 2.13 rad/s2 over a 23.2-s interval?

Answer 1

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;

$\theta = \omega_i \ + \frac{1}{2} \alpha t^2$

the initial angular velocity is zero,

$\theta =0\ + \frac{1}{2} (2.13) (23.2)^2\\\\\theta = 573.2256 \ Rad$

Find how many revolutions that are in 573.2256 Rad

$N = \frac{\theta}{2 \pi} = \frac{573.2256}{2\pi} \\\\N = 91 \ revolutions$

Therefore, the automobile tire rotates 91 revolutions