Electric toothbrushes can be effective in removing dental plaque. One model cons

Question

Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.1 cm in diameter. In one cycle the brush head rotates forward 71.0 and then back. The brush head completes 7700 cycles per minute. The rim of the head contains a thin row of bristles. (See (Figure 1) .) 1.) What is the average angular speed in each direction of the rotating head? 2) What is the average linear speed in each direction of the bristles against the teeth? express both answersin 2 significant figures

Explanation / Answer

(a) Tooth brush is moving 71 degree forward and 71 degree backward that means
in one cycle tooth brush is moving = 71+71 = 142 degree
toothbrush is completing 7700 cycle in one minute
In one cycle , degree covers = 142
In one cycle , angular distance in rad = 142*(Pi/180) = 2.478 rad
In 7700 cycle , = 7700*2.478 rad
7700 cycle is covering in 1 minute , therefore
In 1 minute distance covered = 7700*2.478 rad
therefore in 60 s distance covereed = 7700*2.478 rad
in 1 s = (7700*2.478)/60 = 318.057 rad
Hence the angular speed = 318.057 rad/s
(b) Wwe know that linear speed (v) = angular speed*radius of roatation
v = 318.057*(1.1*0.5) = 174.93 cm /s
v = 1.7493 m/s

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