A ceiling fan of radius 1.0 m is rotating with a frequency of 300 RPM. How fast (in m/sec) is the tip of one of the blades moving?
300 rev/min (2 pi radians/rev)(1 min/60s)
=31.4 radians/second
31.4 rad/s * 1 m = 31.4 meters/second
To determine how fast the tip of one of the ceiling fan blades is moving, we need to calculate the linear velocity.
To find the linear velocity (speed), we'll use the formula:
v = r * ω
where
v is the linear velocity,
r is the radius of the ceiling fan blade, and
ω (omega) is the angular velocity.
To convert the angular velocity from RPM (revolutions per minute) to radians per second, we divide by 60:
ω = (300 RPM) * (2π rad/rev) / (60 sec/min)
Now, substituting the given values into the formula:
v = (1.0 m) * [(300 RPM) * (2π rad/rev) / (60 sec/min)]
Simplifying further, we have:
v = (1.0 m) * [(300 * (2π)) / 60] m/sec
Calculating this expression gives us the answer to the question.