How Fast Do Toothbrush Bristles Move?

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The discussion focuses on estimating the speed of toothbrush bristles during manual brushing. It suggests measuring the radius of the toothbrush to calculate the speed using the formula v = rω. The angle of 45° is converted to radians, leading to the calculation of angular velocity (ω) as 5/4π radians per second. Participants are encouraged to apply these calculations to determine the approximate speed of the bristles against the teeth. This analysis highlights the relationship between the toothbrush's motion and the effectiveness of brushing.
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Homework Statement


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° five times per second)


Homework Equations



ω=Δθ/Δt v=rω

The Attempt at a Solution


I'm not sure where to start
 
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As you say, v= r\omega. Go get your toothbrush and measure it to get "r". 45° is 360/45= 1/8 of a complete circle (2\pi radians) so \omega= (5/8)2\pi= (5/4)pi rad per second.
 

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