Question

1. determine the angular acceleration of a gear that speeds up from 25 rpm to 45 rpm in 3 seconds.

$ -0.70 \frac{\text{rad}}{\text{s}^2} $
$ 0.70 \frac{\text{rad}}{\text{s}^2} $
$ 0.35 \frac{\text{rad}}{\text{s}^2} $
$ 1.4 \frac{\text{rad}}{\text{s}^2} $

Explanation:

Step1: Convert RPM to rad/s

Initial angular velocity: $\omega_0 = 25 \times \frac{2\pi}{60} = \frac{5\pi}{6} \approx 2.618 \ \text{rad/s}$
Final angular velocity: $\omega = 45 \times \frac{2\pi}{60} = \frac{3\pi}{2} \approx 4.712 \ \text{rad/s}$

Step2: Calculate angular acceleration

Angular acceleration formula: $\alpha = \frac{\omega - \omega_0}{t}$
Substitute values: $\alpha = \frac{4.712 - 2.618}{3} \approx \frac{2.094}{3} \approx 0.70 \ \frac{\text{rad}}{\text{s}^2}$

Answer:

0.70 $\frac{\text{rad}}{\text{s}^2}$