Question

An electric motor of 12 horsepower generates an angular velocity of 125 radians per second. What will be the frequency of rotation?

$$\begin{gathered} A.20Hz \\ B.{\displaystyle \frac{20}{\pi }}Hz \\ C.{\displaystyle \frac{20}{2\pi }}Hz \\ D.40Hz \end{gathered}$$

Answer 1

Hint: Angular velocity of the motor is the rate of rotation of the conductors associated in the motor with respect to time. It is denoted by $\omega$ and is abbreviated as omega. It is measured in radians per seconds. The frequency is the rate at which the conductor occupies the pre-defined space in the motor. It is denoted by f and is measured in Hertz.

Here in the question, we need to determine the frequency of rotation of the motor such that the angular velocity of the electric motor is given as 125 radians per seconds. For this, we will use the general relation between the angular speed and the frequency as $\omega =2\pi f$.

Complete step by step answer:
The angular velocity of the conductor in an electric motor is the product of the frequency of the rotation of the motor and the total circular radian. Mathematically, $\omega =2\pi f$ where, $\omega$ is in radian per seconds and $f$ is in Hertz.

Here, $\omega =125\text{ rad/sec}$ so, substituting the same in the formula $\omega =2\pi f$ to determine the frequency of rotation.

$$\begin{gathered} \omega =2\pi f \\ 125=2\pi f \\ f={\displaystyle \frac{125\times 7}{2\times 22}} \\ ={\displaystyle \frac{875}{44}} \\ =19.88\text{ Hz} \\ \approx \text{20 Hz} \end{gathered}$$

Hence, the frequency of rotation of an electric motor of 12 horsepower generates an angular velocity of 125 radians per second is 20 Hz.

Option A is correct.


Note: It is interesting to note here that the power rating of the electric motor has been given in the question is of no use. It is just added as an added information