Question

Dizziness. Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose a dancer (or skater) is spinning at a very fast 2.9 revolutions per second about a vertical axis through the center of his head. Although the distance varies from person to person, the inner ear is approximately 7.0 cm from the axis of spin.What is the radial acceleration (in m/s^2 ) of the endolymph fluid?

Answer 1

`23.2 m/s^2`

Step-by-step explanation:

First of all, we need to convert the angular velocity from revolutions per second to radiands per second. We know that

`1 rev = 2 \pi rad`

So
`\omega = 2.9 rev/s \cdot 2\pi rad/rev =18.2 rad/s`

We also know that the distance of the inner ear from the centre of the circular path is

`r = 7.0 cm = 0.07 m`

the radial (centripetal) acceleration experienced by a point on the inner ear is

`a=\omega^2 r`

Therefore, substutiting the previous values, we find the radial acceleration of the endolymph fluid:

`a=(18.2)^2(0.07)=23.2 m/s^2`