How Fast Do Toothbrush Bristles Move?

[phyhelp]

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

 

[HallsofIvy]

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.