Angular Speed of Electric Toothbrush Head: 795.49rad/s

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SUMMARY

The discussion centers 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 due to misunderstanding the rotation's nature. The correct average angular speed should account for the back-and-forth motion, effectively doubling the angular speed calculation to reflect the total movement in both directions.

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  • Ability to perform unit conversions (minutes to seconds)
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  • Learn about angular velocity calculations in rotational dynamics
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Engineers, physics students, and anyone interested in the mechanics of electric toothbrushes or rotational motion principles will benefit from this discussion.

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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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