# Velocity of a toothbrush?

1. Jun 6, 2012

### phyhelp

1. The problem statement, all variables and given/known data
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)

2. Relevant equations

ω=Δθ/Δt v=rω

3. The attempt at a solution
I'm not sure where to start

2. Jun 6, 2012

### 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.