Question

The angular speed of a flywheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s² is:

• A. \(2\pi\)
• B. \(4\pi\)
• C. \(12\pi\)
• D. \(104\pi\)

Answer 1

The Correct Option is B

We have two rotational velocities:
\(ω_1\), which is 1200 revolutions per minute, and \(ω_2\), which is 3120 revolutions per minute.
We also know that the time it takes for the rotation to go from \(ω_1\) to \(ω_2\) is 16 seconds.
Using this information, we can calculate the angular acceleration \((\alpha)\) of the rotation as follows:

\(\alpha = [\frac{(ω_2 - ω_1)}{t}] \times [\frac{2\pi}{60}]\)
\(\alpha = [\frac{(3120 - 1200)}{16}] \times [\frac{2\pi}{60}]\)
\(\alpha = (\frac{1920}{16}) \times (\frac{2\pi}{60})\)
\(\alpha = 4\pi\)

Therefore, the angular acceleration is 4π radians per second squared.