1. Given data

• Initial angular speed of wheel: $900\ \text{rpm}$
• Final angular speed of wheel: $2460\ \text{rpm}$
• Time taken: $26\ \text{s}$
• Angular acceleration is uniform.

We need the number of revolutions during this interval.

2. Use average angular speed

For uniform angular acceleration,

$\omega_{\text{avg}}=\frac{\omega_i+\omega_f}{2}$

So,

$\omega_{\text{avg}}=\frac{900+2460}{2}=\frac{3360}{2}=1680\ \text{rpm}$

3. Convert time into minutes

Since speed is in rpm, convert $26$ s into minutes:

$t=\frac{26}{60}=\frac{13}{30}\ \text{min}$

4. Find number of revolutions

Number of revolutions = average rpm $\times$ time in minutes:

$N=1680\times \frac{13}{30}$

$N=56\times 13=728$

5. Final answer

$\boxed{728}$

6. Comparison with stored correct answer

Stored correct answer = $728$

Our derived answer also is $728$, so they agree.