Question

The blades of an aeroplane propeller are 2m long and rotate at 300 rpm.calculate angular velocity and linear velocity of a point on the blades 0.5 m from the tip of the blades

Answer 1

The blades make 300 revolutions per minute.

Revolutions per second is :

300 / 60 = 5 revolutions per second.

One revolution = 2π

Hence : 5 × 2π = 10π

Angular velocity = 10 π radians / second

Linear velocity = rw where

w = angular velocity

r = radius from the center

r = 12 - 0.5 = 11.5

V = 11.5 × 10π = 115π

361.28 m/s

Answer 2

Please find the answer below:

Keeping in view that, the blades of an aeroplane propeller are 2m long and rotate at 300 rpm. The angular velocity and linear velocity of a point on the blades 0.5 m from the tip of the blades is I1 *w1 = I2 *w2

Explanation:

Conserve angular momentum for w at 0.5 m from the tip.

I1 w1 = I2 w2

ml^2/3 * 300 = m(0.25l)^2/3 * w

Get the value of 'w' from here.

For,

Time period; T = 2pi/w

Frequency, f = 1/T

and

Linear velocity v = w*x (where x = 1.5 m from hinge)