Angular Speed of Electric Toothbrush Head: 795.49rad/s

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The discussion focuses on calculating the average angular speed of an electric toothbrush head that rotates back and forth through a 70-degree angle at a rate of 7600 times per minute. The initial calculation of 795.49 rad/s is incorrect because it assumes a full rotation instead of the specified angle. The correct approach involves converting the 70 degrees to radians and considering the time for each back-and-forth cycle. If the toothbrush head rotates 70 degrees in one direction and then returns, the angular speed would effectively be doubled. The clarification emphasizes the importance of understanding the motion's direction and the angle involved in the calculation.
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Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.10cm in diameter that rotates back and forth through a 70.0 angle 7600times/min . The rim of the head contains a thin row of bristles. its asking me the average angular speed in each direction of the rotating head.

w=7600times/min(1min/60s)6.28rad/1rev= 795.49rad/s

but it says I am wrong what am i doing wrong?
 
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It rotates through 70deg 7600 times /minute not a full circle.
so that's 70 * pi/180 radians in 60/7600 seconds.

It could also be double that if it means it goes +70deg then back to the start 7600 times a minute?
 
yea it would be double since its going back and forth thanks
 
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