Mechanical Power

Calculate the mechanical power (W) of a 20 N∙m motor if its rotational speed is 3,600 rpm.

Expand Hint
Mechanical power in a rotating machine:
$$$P=T \omega_m$$$
where $$T$$ is the mechanical torque, and $$w_m$$ is the angular velocity.
Hint 2
The relationship between angular velocity (rad/s) and speed in rpm is:
$$$\omega_m=\frac{2\pi}{60}n$$$
where $$n$$ is the motor’s speed in rpm.
Mechanical power in a rotating machine:
$$$P=T \omega_m$$$
where $$T$$ is the mechanical torque, and $$w_m$$ is the angular velocity.

Since angular velocity is in rad/s, let’s convert the rotational speed from the problem statement:
$$$\omega_m=\frac{2\pi}{60}n$$$
where $$n$$ is the motor’s speed in rpm.
$$$\omega_m=\frac{2\pi}{60}\cdot 3,600=376.8\:rad/s$$$
Thus,
$$$P= (20N\cdot m)(376.8\:rad/s)=7,536\:W$$$
7,536 W