Our balance is maintained, at least in part, by the endolymph fluid in the inner

Question

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 2.6 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?


What is the radial acceleration (in g's) of the endolymph fluid?

Explanation / Answer

The radial velocity of the fluid is ( )   = 2.6 rev / s                                                                    = (2.6 rev / s ) ( 2 rad / 1 rev )                                                                   = 5.2 rad / s The radius of the circular path is ( r ) = 7.0 cm                                                               = ( 7.0 cm ) ( 10-2 m / 1 cm )                                                               = 7.0*10-2 m The radial acceleration can be defined as                                                         a = 2r                                                                                                                         = ( 5.2 rad / s )2 ( 7.0*10-2 m )                                                              = 18.7 m / s2 The radial acceleration interms of acceleration due to gravity (g ) = 9.8 m/s2 is                                                        a = ( 18.7 m / s2 ) ( 1 g / ( 9.8 m/s2 )                                                           = 1.91 g                                                                    = (2.6 rev / s ) ( 2 rad / 1 rev )                                                                   = 5.2 rad / s The radius of the circular path is ( r ) = 7.0 cm                                                               = ( 7.0 cm ) ( 10-2 m / 1 cm )                                                               = 7.0*10-2 m The radial acceleration can be defined as                                                         a = 2r                                                                                                                         = ( 5.2 rad / s )2 ( 7.0*10-2 m )                                                              = 18.7 m / s2 The radial acceleration interms of acceleration due to gravity (g ) = 9.8 m/s2 is                                                        a = ( 18.7 m / s2 ) ( 1 g / ( 9.8 m/s2 )                                                           = 1.91 g

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