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 in diameter that rotates back and forth through a 70.0 angle 7600 times per minute. The rim of the head contains a thin row of bristles. (See the figure )Assuming that the toothbrush has constant angular acceleration in each of the directions it turns, find the angular acceleration (in ) of the rotating head and the tangential acceleration (in ) of the bristles.

Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.1 in diameter that rotates back and forth through a 70.0 angle 7600 times per minute. The rim of the head contains a thin row of bristles. (See the figure )Assuming that the toothbrush has constant angular acceleration in each of the directions it turns, find the angular acceleration (in ) of the rotating head and the tangential acceleration (in ) of the bristles. alphatan in m/s^2? alpha in rad/s^2? What is What is

Explanation / Answer

Number of back and forth motions per second is7600times/min Therefore time for one motion is                                 =(1/7600)min                                 =7.8948*10-3s Time for either back or forth motion is                        t =7.894*10-3s/2                             =3.947*10-3s a) But the angular displacement in one motion is70 degrees =700            =0.388 rad the angular speed =/t                                = 0.388/3.947*10-3                                = 309rad/s therefore the anggular accelaration,            = /t                = 309/3.974*10^-3                = 236.2*10^3 rad/s^2 b) The average linear speed (v) =r Then r is the radius of the head =1.1cm/2 = 0.55cm Then the speed (v) = (0.55cm)(309rad/s)                              =1.6995m/s                              =1.7m/s the tangential acceleration, a = v/t            a = 1.7/3.974*10^-3               = 427.78 m/s^2                                = 309rad/s therefore the anggular accelaration,            = /t                = 309/3.974*10^-3                = 236.2*10^3 rad/s^2 b) The average linear speed (v) =r Then r is the radius of the head =1.1cm/2 = 0.55cm Then the speed (v) = (0.55cm)(309rad/s)                              =1.6995m/s                              =1.7m/s the tangential acceleration, a = v/t            a = 1.7/3.974*10^-3               = 427.78 m/s^2

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