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
Time Analysis
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