How Fast Do Bristles on an Electric Toothbrush Move?

[merlos]

Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.10 cm in diameter that rotates back and forth through a 70.0 degree angle 7600 times/min. The rim of the head contains a thin row of bristles.

Part A: What is the average angular speed in each direction of the rotating head, in rad/sec?

(140degrees)(pi/180) = 2.44 rad/rev

w = (7600 rev/min)(1min/60sec)(2.44rad/1rev) = 310 rad/sec


Part B What is the average linear speed in each direction of the bristles against the teeth?

A little unsure of

v = rw
v = (.006m)(310rad/sec)
v = 1.85 m/s

 

[Doc Al]

Your method looks OK. To avoid round-off errors in your arithmetic, don't round off until the very last step.