Question

a fan rotates at 100 round per minute. find the angular velocity and linear velocity if tip of it blades is 20 CM away from it axis of rotation.

Answer 1

Number of revolution = 100 rounds in 1 minute

frequency = Number of revolutions per seconds

$Frequency = \frac{100}{60}$ Hz

Frequency (f) = 1.67 Hz

Let the angular velocity be ω

ω = 2$\pi$f

ω = 2 × 3.14 × 1.67

ω = 10.49 rad/sec

Hence, the angular velocity of the fan is 10.49 rad/sec

Now, let the linear velocity be v.

v = ω × r

r = 20 cm = 0.2 m

v = 10.49 × 0.2

v = 2.098 m/s

Hence, the linear velocity of the fan is 2.098 m/s

Answer 2

Number of revolution = 100 rounds in 1 minute

frequency = Number of revolutions per seconds

Hz

Frequency (f) = 1.67 Hz

Let the angular velocity be ω

ω = 2f

ω = 2 × 3.14 × 1.67

ω = 10.49 rad/sec

Hence, the angular velocity of the fan is 10.49 rad/sec

Now, let the linear velocity be v.

v = ω × r

r = 20 cm = 0.2 m

v = 10.49 × 0.2

v = 2.098 m/s

Hence, the linear velocity of the fan is 2.098 m/s