# What is the radial acceleration of the endolymph fluid in m/s^2 and as a multiple of g?Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this...

What is the radial acceleration of the endolymph fluid in m/s^2 and as a multiple of g?

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 3.0 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.

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### 1 Answer

A dancer is spinning at a very fast 3.0 revolutions per second about a vertical axis that passes through the center of his head. The distance from the axis of spin to the inner ear is approximately 7.0 cm.

The radial acceleration is given by a = v^2/r = w^2*r where w is the angular velocity is radians/second. As the dancer rotates at 3 revolutions per second the angular velocity is 2*pi*3 = 6*pi radians/sec

a = 36*pi^2*7/100 m/s^2

=> 24.87 m/s^2

The acceleration of 1 g = 9.8 m/s^2

24.87 m/s^2 = 24.87/9.8 = 2.53 g

The radial acceleration of the fluid in the ear of the dancer is 24.87 m/s^2 or 2.53 g

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