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problem reference 8 - 2
on an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. the seats begin from rest and are uniformly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s.
what is the tangential acceleration of the passengers during the first 21 s of the ride?
29 m/s²
0.0089 m/s²
0.50 m/s²
220 m/s²

Explanation:

Step1: Find angular acceleration

Angular acceleration $\alpha$ is change in angular velocity over time. Initial angular velocity $\omega_0 = 0$, final $\omega = 1.4$ rad/s, time $t = 21$ s. So $\alpha=\frac{\omega - \omega_0}{t}=\frac{1.4 - 0}{21}=\frac{1.4}{21}=\frac{1}{15}\approx0.0667$ rad/s².

Step2: Find tangential acceleration

Tangential acceleration $a_t = r\alpha$, where $r = 7.5$ m. So $a_t = 7.5\times\frac{1}{15}= 0.5$ m/s².

Answer:

0.50 m/s² (corresponding to the option "0.50 m/s²")