Questions: A typical angular speed of an AC induction electric motor is 3600 rpm. Convert this speed to radians per second. Use 2 conversion factors to change rpm to angular speed. ω=

Solution Steps

We need to convert the angular speed of an AC induction electric motor from revolutions per minute (rpm) to radians per second (rad/s).

1. There are \(2\pi\) radians in one revolution.
2. There are 60 seconds in one minute.

Given: \[ \text{Angular speed} = 3600 \, \text{rpm} \]

First, convert rpm to revolutions per second (rps): \[ 3600 \, \text{rpm} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}} = 60 \, \text{rps} \]

Next, convert revolutions per second to radians per second: \[ 60 \, \text{rps} \times 2\pi \, \text{radians per revolution} = 120\pi \, \text{rad/s} \]

\[ 120\pi \approx 120 \times 3.1416 = 376.9911 \, \text{rad/s} \]

Final Answer