Question

A disk at rest experiences a constant angular acceleration for t = 85 s, at the end of which it is spinning with a frequency of f = 15 rpm. What is the angular acceleration of the disk?

1) 0.176 rad/s²
2) 0.314 rad/s²
3) 0.530 rad/s²
4) 0.942 rad/s²

Answer 1

Using the relationship between angular velocity and angular acceleration, the calculated angular acceleration is 0.0185 rad/s², which does not match the given options, suggesting a possible error in the question or options.

Step-by-step explanation:

The angular acceleration of the disk can be calculated using the formula α = Δω/Δt, where α is the angular acceleration, Δω is the change in angular velocity, and Δt is the change in time. First, we need to convert the frequency f = 15 rpm to radians per second. Since 1 revolution is 2π radians and there are 60 seconds in a minute, the angular velocity ω is 15 rev/min × (2π rad/rev) / (60 s/min) = 1.57 rad/s. Because the disk started from rest, the change in angular velocity Δω is 1.57 rad/s. Given the time t = 85 s, we calculate the angular acceleration (α) as α = 1.57 rad/s / 85 s = 0.0185 rad/s². This value does not match any of the options provided. Therefore, if we strictly follow the options given in the question, none of the options would be correct, suggesting there might be an error in the question or the provided options.