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 1.10 cm in diameter that rotates back and forth through a 70.0 degrees angle 7600 times per minute. The rim of the head contains a thin row of bristles.

Part A: What is the average angular speed in each direction of the rotating head, in rad/s?

Part B: What is the average linear speed in each direction of the bristles against the teeth? (to two sig. figures)

Part C: Using your own observations, what is the approximate speed of the bristles against your teeth when you brush by hand with an ordinary toothbrush? (Estimate that the toothbrush turns back and forth through 45 degrees five times per second) (in cm/s, two sig. figures).

Explanation / Answer

This is 140 degree (note the brush goes first 70 degrees forward followed by 70 degrees backwards) * 7600 /min

= 140 deg*7600/Min * 1 min/ 60 sec

= 17733 deg/sec.

The average absolute linear speed of the outside rim of the toothbrush is:

Average Angular velocity *2pi*r/360deg
r=d/2
=17333 deg/sec *pi*d/360deg
=17333 deg/sec * pi * 1.1 cm /360 deg
=170 cm/sec
=1.7 m/sec

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