Question

The shaft of a motor rotating at \(50\) rev s\(^{-1}\) is uniformly retarded to \(20\) rev s\(^{-1}\) in \(15\) s. The number of complete rotations the shaft makes in the given time is . (Answer in integer)

Hint:

Since the retardation is uniform, the angular speed falls linearly, so the average speed times the time gives the total rotations.

Answer 1

Correct Answer: 525

Step 1: Note what uniform retardation means.
Uniform retardation means the angular speed decreases at a constant rate with time, just like uniform deceleration in straight-line motion. For such motion, the angular speed changes linearly from the initial value to the final value.

Step 2: Use the average angular speed to find total rotations.
Because the speed drops linearly, the average speed over the interval is simply the mean of the initial and final speeds.
\[ N_{avg} = \frac{N_i + N_f}{2} = \frac{50 + 20}{2} = 35 \text{ rev/s} \]
The total number of rotations equals this average speed multiplied by the time taken.
\[ n = N_{avg} \times t \]

Step 3: Substitute the values.
\[ n = 35 \times 15 = 525 \]

Final Answer:
The shaft makes 525 complete rotations while its speed drops from 50 rev/s to 20 rev/s in 15 s.
\[ \boxed{n = 525} \]