An 80.4 kg propeller blade measures 2.03 m end to end. Model the blade as a thin

Question

An 80.4 kg propeller blade measures 2.03 m end to end. Model the blade as a thin rod rotating about its center of mass. It's initially turning at 185 rpm.

(a) Find the blade's angular momentum. Express your answer with the appropriate units.

(b) Find the tangential speed at the blade tip. Express your answer with the appropriate units.

(c) Find the angular acceleration required to stop the blade in 11.0 s. Express your answer with the appropriate units.

(d) Find the torque required to stop the blade in 11.0 s. Express your answer with the appropriate units.

Explanation / Answer

mass, M= 80.4 kg

radius, l = 2.03 m

o = 185rpm = 185 *0.1047 rad/s = 19.3rad/s

a) Angular momentum , L = I

where I = 1/12Ml^2 = (1/12)*80.4 kg *(2.03 m)^2

         I = 27.6 kg m^2

L = 27.6 kg m^2 *19.3 rad/s

L = 532.8 Js

b) Tangential speed , v = r = (2.03/2) *19.3 rad/s

   v =19.5 m/s

c)Angular acceleration , = ( -o)/t

                                       = (0 - 19.3 rad/s)/11s

                      = -1.75 rad/s^2

d)Torque = I = 27.6 kg m^2 * 1.75 rad/s^2 = 48.3 N.m

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