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

CONCEPT:

According to the uniform circular motion, the equation of motion is written as;

ω = ω_o + α t

Here, ω is the final angular speed, ωo the initial angular speed, t is the time taken, α is angular acceleration.

CALCULATION:

Given:  initial angular speed ωo  = 1200 rpm

final angular speed, ω = 3120 rpm

t = 16 sec.

The initial angular speed, ωo = 1200 rpm

 ωo = \(\frac{2 π \times 1200}{60}\)

= 40 π  rad/sec.

Similarly, 

The final angular speed  ω = 3120 rpm

= \(\frac{2 π \times 3120}{60}\)

= 104π  rad/sec.

Now, using ω = ωo + α t  which is

\(α =\frac{ω -ω _o }{t}\)

⇒ \(α =\frac{104 π -40 π}{16}\)

⇒ \(α\) = 4π rad/s²

Hence option 3) is the correct answer.