Rotating fan - explanation to physics problem
A fan rotates at 1500 rpm (revolutions per minute). What is the speed of a point on a blade 10cm from the axis. What is the period (in SI units) of the motion? What is the speed of this point on the blade. What distance does the point move during 1.0 hour?
Given:
f = 1500 rpm – number of revolutions per minute
R = 10cm – radius of a point on the blade
t = 1h – time of rotation of a fan
We are looking for:
T = ? – period of motion
v = ? – speed of the point on the blade
D = ? - total distance traveled during 1 h.
We write some formulas
v = 2πR/T (1)
T = 1/f (2)
D= vt (3)
Formulas (1) and (2) describe uniform circular motion. Formula (3) is from linear motion.
Substituting (2) into (1) we get
v = 2πRf (4)
Wit this relation
D = 2πRft (5)
And the period in SI units is
Speed is
We recalculate this speed into km/h, and miles/hour to get some comparison with cars speed
The total distance traveled during 1.0 hour is, in accordance with formula (3)
D = 56.5km = 35.1 mile