Question

electric toothbrushes can be effective in removing dental plaque. one model consists of a head 1.1 cm in diameter that rotates back and forth through a 70 angle 7600 times per minute. what is the average angular speed in each direction of the rotating head?

Answer 1

`\omega=309.44\ rad/s`

Step-by-step explanation:

It is given that, one model consists of a head 1.1 cm in diameter that rotates back and forth through a 70 angle 7600 times per minute.

In one cycle, the head turns through 140 degrees i.e. 2.443 radian. In one minute, it turns through,
`\theta=7600* 2.443=18566.8\ rad`

Let
`\omega` is the average angular speed in each direction of the rotating head. It is given by :

`\omega=(\theta)/(t)`

`\omega=(18566.8\ rad)/(60\ s)`

`\omega=309.44\ rad/s`

So, the average angular speed in each direction of the rotating head is 309.44 rad/s. Hence, this is the required solution.