## Mechanical Power

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

##
__
__**Expand Hint**

**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**

**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

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