Question

A large ceiling fan has blades of radius equal to 71 cm. When you switch this fan on, it takes 18 s to attain its final steady speed of 0.8 rev/s. Assume a constant angular acceleration.

(a) What is the angular acceleration of the fan? rad/s^2

(b) How many revolutions does it make in the first 18 s? rev

(c) What is the distance covered by the tip of one blade in the first 18 s? m

Answer 1

here,

radius, r = 0.71 m

t = 18 s

a)fianl angular velocity, wf = 0.8 rev/s = 5.03 rad/s

for the angular acceleration

angular acceleration = change in angular speed/time

angular acceleration = (5.03 - 0)/18

angular acceleration = 0.28 rad/s^2

the angular acceleration is 0.28 rad/s^2

b)

for the angle

angle = 0.50 * a* t^2

angle = 0.50 * 0.28 * 18^2

angle = 45.4 rad = 7.22 rev

the number of revs made is 7.22 rev

c) distance covered = angle * radius

distance covered = 0.71 * 45.4

distance covered = 32.23 m

the distance covered is 32.23 m