Question

A motor rotates at a constant speed of 25 revolutions per second. What is the power derived by the motor if it supplies a torque of 60 Nm?
A. $2500\,W$
B. $1500\pi \,W$
C. $1250\,W$
D. $3000\pi \,W$

Answer 1

Hint: Torque is defined as rotational or twisting force. It is the measure of force required to rotate an object about an axis.
Power in rotational motion is equivalent to the product of torque and angular frequency.

Formula used: Power of a rotating body, $P=\tau \omega $

Complete step by step answer:
Torque is defined as the rotational equivalent of force required to rotate an object about an axis. Torque on an object is denoted by $\tau$. Torque is a vector quantity.
We are provided that the motor rotates with a speed of 25 revolutions per second. This is the frequency of the motor.
$f=25\,rev/s$
Power of a body is defined as the amount of energy converted per unit time. Its SI unit is joule per second or watt.
Power of a body in rotational motion is equivalent to product of torque and its angular frequency. It is expressed as
$P=\tau \omega $
Where $\tau$ denotes the torque and $\omega$ is the angular frequency
Angular frequency of a rotating body is its angular displacement per unit time. It is related to frequency of the body by relation
$\omega =2\pi f$
Since, $f=25rev/s$. This implies that $\omega =2\pi f=2\pi \times 25=50\pi \,rad/s$
Torque supplied by the motor is $60Nm$.
Therefore, Power used by the motor is
$P=60\times 50\pi =3000\pi \,Watt$

So, the correct answer is “Option D”.

Note: Power of a body is defined as amount of energy converted per unit time. Its SI unit is joule per second or watt. Power of a body in rotational motion is equivalent to product of torque and its angular frequency.
Angular frequency is related to frequency of the body by relation
$\omega =2\pi f$