A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is ___________.

Solution

Physics sir · 3 steps

Uniform angular acceleration means you can use the average speed: average rps times time gives the rotations.

1. Convert to rps. The time is in seconds, so change rpm to rotations per second. 600 rpm = 10 rps and 1800 rpm = 30 rps.
2. Average speed. With uniform acceleration the speed rises linearly. So the average speed is the mean of the start and end values: (10 + 30)/2 = 20 rps.

   N = ((n₁ + n₂)/2) t = 20 rps × 10 s

3. So. The body makes N = 200 rotations, so the answer is 200.

The common slip: 12000. Multiplying the average of 1200 rpm by 10 s mixes minutes with seconds and gives 12000. Convert to rps first.

The idea to keep. Rotational motion with constant α works just like linear motion with constant a: angle turned is average angular speed times time. Make the time units match first.

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