Solution:

Given data:

Initial angular velocity, ω1 = 600 rev/min
Final angular velocity, ω2 = 2400 rev/min
Time interval, t = 10 sec

To find:

Number of revolutions made during the time interval.

Formula used:

Angular acceleration (α) = (ω2 - ω1)/t
Number of revolutions made during the time interval = (ω2 + ω1)/2 * t/60

Calculation:

Angular acceleration (α) = (ω2 - ω1)/t
= (2400 - 600)/10
= 180 rad/sec²

Number of revolutions made during the time interval = (ω2 + ω1)/2 * t/60
= (2400 + 600)/2 * 10/60
= 1000 rev

Therefore, the number of revolutions made during the time interval is 1000 rev.

Explanation:

- The given problem is related to the angular velocity of a wheel.
- The angular velocity of a wheel is the rate of change of the angle through which the wheel rotates per unit time.
- The unit of angular velocity is rad/sec or rev/min.
- In the given problem, the initial angular velocity and final angular velocity are given.
- The time interval is also given.
- Using the formula for angular acceleration, the angular acceleration is calculated.
- Using the formula for the number of revolutions made during the time interval, the number of revolutions is calculated.
- The solution is expressed in revolutions.

Conclusion:

The number of revolutions made during the time interval is 1000 rev.