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Chapter 12: Q. 3 (page 330)

A ceiling fan with 80 cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25s after being turned off.

Short Answer

Expert verified

The speed of the tip of the blade is 1.15 m/s

The number of revolutions is 12.5 rev

Step by step solution

01

Step 1. Given information

The diameter of the fan is 80 cm, its angular velocity is 60 rpm , and it needs to 25 seconds to stop.

The radius of the blade is r=40cm,

d=(40cm)0.01m1cm=0.4m

Initial angular speed of the fan is

蝇i=60revmin2蟺rad1rev1min60s=6.28rad/s

The angular acceleration of the fan is,

伪=蝇f鈭�蝇i螖t=0鈭�6.28rad/s25s=鈭�0.251rad/s2

02

Part (a)

The angular speed of the tip of the blade is

蝇f=蝇i+伪t=6.28rad/s+鈭�0.251rad/s2(10s)=3.77rad/s

The speed of the tip of the blade is,

v=r蝇f=(0.4m)(3.77rad/s)=1.51m/s

Therefore, speed of the tip of the blade is 1.51m/s.

03

Part (b)

The number of revolutions, in螖t=25s

螖胃=蝇i螖t+12伪螖t2=6.28rad/s25s+12鈭�0.251rad/s225s2=78.6rad1rev2蟺rad=12.5rev

Therefore, the number of revolutions is12.5rev

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