Question

question 25
4 points
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a ball attached to a string starts at rest and undergoes a constant angular acceleration as it travels in a horizontal circle of radius 0.30 m. after 0.65 sec, the angular speed of the ball is 9.7 rad/s. what is the tangential acceleration of the ball?
7.6 m/s²
4.5 m/s²
0.32 m/s²
15 m/s²
28 m/s²

Explanation:

Step1: Calculate angular acceleration

Initial angular speed $\omega_0 = 0$, final $\omega = 9.7$ rad/s, time $t = 0.65$ s.
$\alpha = \frac{\omega - \omega_0}{t} = \frac{9.7 - 0}{0.65} \approx 14.923$ rad/s²

Step2: Calculate tangential acceleration

Radius $r = 0.30$ m.
$a_t = r\alpha = 0.30 \times 14.923 \approx 4.5$ m/s²

Answer:

4.5 m/s²