Brake Power

Calculate the brake power (Watts) if the force applied at the end of the 3 m long brake arm is 250 N, and the rotation speed is 1100 rpm.

Hint
Brake Power:
$$$\dot{W}_b=2\pi \tau \upsilon =2\pi FR\upsilon $$$
where $$\tau$$ is torque, $$\upsilon $$ is rotational speed, $$F$$ is the force at the end of the brake arm, and $$R$$ is the brake arm’s length.
Hint 2
Convert the rotational speed from rpm to rev/s:
$$$\upsilon =1100\: \frac{rev}{min}\cdot \frac{1\:min}{60\:secs}=18.33\:\frac{rev}{s}$$$
Brake Power:
$$$\dot{W}_b=2\pi \tau \upsilon =2\pi FR\upsilon $$$
where $$\tau$$ is torque in $$N \cdot m$$ , $$\upsilon $$ is rotational speed in $$rev/sec$$ , $$F$$ is the force at the end of the brake arm, and $$R$$ is the brake arm’s length. Thus,
$$$\tau = 250\:N\cdot 3\:m=750\:N\cdot m$$$
$$$\upsilon =1100\: \frac{rev}{min}\cdot \frac{1\:min}{60\:secs}=18.33\:\frac{rev}{s}$$$
Finally,
$$$\dot{W}_b=(2\pi )(750\:N\cdot m)(18.33\:\frac{rev}{s})=86,350\:W$$$
86,350 W