The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time is _____________. (Assuming the acceleration to be uniform).

Solution

Physics sir · 3 steps

Uniform acceleration means the average speed is the midpoint, so revolutions are average rps times time.

1. Convert to rps. The time is in seconds, so change rpm to revolutions per second. 900 rpm = 900/60 = 15 rev s⁻¹ and 2460 rpm = 2460/60 = 41 rev s⁻¹.
2. Average speed. When the angular acceleration is uniform, the speed rises linearly. So the average speed is the mean of the start and end values, just as in linear motion with s = (u+v)/2t.

   N = (n₁ + n₂)/2 t = (15 + 41)/2 × 26 = 28 × 26

3. So. N = 728 revolutions. In radians this is θ = 1456π rad, and 1456π / 2π = 728 gives the same answer. The answer is 728.

The common slip: 43680. Using 900 and 2460 rpm directly with 26 seconds, without dividing by 60, gives 1680 × 26 = 43680, not 728.

The idea to keep. Rotational kinematics follows the same rules as linear kinematics. With uniform angular acceleration, angle turned = average angular speed × time. Match the time units before you multiply.

Answer from the NTA final answer key. Solution by PrepWiser.