The motor of a fan turns a small wheel of radius rm = 1.60 cm.This wheel turns a belt, which is attached to a wheel of radius rf = 2.90 cmthat is mounted to the axle of the fan blades. Measured from the center of this axle, the tip of the fan blades are at a distance rb = 11.0 cm.When the fan is in operation, the motor spins at an angular speed of ù = 1200 rpm. What is the tangential speed of the tips of the fan blades?
tangential velocity = (blade radius)*w
where w is the angular velocity of the fan blades (not the motor) in radians/s. Get it from the motor's rpm and the ratio 2.90/1.60. That is the ratio of motor rpm to blade rpm in this case.
Thanks for the help drwls. I got the correct answer, but the ratio was suppose to be 1.60/2.90.
You are quoting the inverse rotary speed ratio, blade/motor. It all depends upon whether you multiply or divide the factor. We do not disagree.
To find the tangential speed of the tips of the fan blades, we can use the formula:
Tangential speed = radius x angular speed
First, let's convert the angular speed from rpm (revolutions per minute) to radians per second. Since 1 revolution is equal to 2π radians, we can use the conversion factor:
1 revolution/1 minute = 2π radians/60 seconds
So, the angular speed in radians per second is:
ù = (1200 rpm) x (2π radians/60 seconds) = 40π radians/second
Now, we can substitute the values into the formula:
Tangential speed = (radius of the belt wheel) x (angular speed)
The radius of the belt wheel is given as rf = 2.90 cm.
Tangential speed = (2.90 cm) x (40π radians/second)
To get the answer in a different unit, such as meters per second, we'll need to convert the centimeters to meters. Since there are 100 centimeters in 1 meter, we divide the cm value by 100:
Tangential speed = (2.90 cm / 100) x (40π radians/second)
Now, we can calculate the tangential speed using a calculator:
Tangential speed ≈ (0.029 meters) x (40π radians/second) ≈ 1.16π meters/second
To get a numerical value for the answer, we can approximate the value of π as 3.14:
Tangential speed ≈ 1.16 x 3.14 ≈ 3.64 meters/second
Therefore, the tangential speed of the tips of the fan blades is approximately 3.64 meters per second.