Question

Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose that a skater is spinning very fast at 3.0 revolutions per second about a vertical axis through the center of his head. Take the inner ear to be approximately 7.0 cm from the axis of spin. (The distance varies from person to person.) What is the radial acceleration (in m/s2 and in g’s) of the endolymph fluid?

Answer 1

Answer:

Acceleration=a=24.9 m/s^2≅$25\ m/s^2$

Acceleration in g's:

Acceleration=24.9/9.8=2.54 g's

Explanation:

Given:

Revolutions= 3.0 revolutions per second

Distance from the axis of spin=7.0 cm=0.07 m

Required:

Radial acceleration (in m/s^2 and in g’s) of the endolymph fluid=?

Solution:

Time for one revolution:

T=1/3 rev=0.333 sec

Distance= Speed*Time

Speed=Distance/Time

Distance=2πR

$Speed=v=\frac{2\pi R}{T}\\Speed=v=\frac{2\pi*0.07}{0.333} \\Speed=v=1.32079 m/s$

Acceleration in circular Path:

$a=\frac{v^2}{R} \\a=\frac{1.32079^2}{0.07}\\a= 24.9 m/s^2$

Acceleration=a=24.9 m/s^2≅$25\ m/s^2$

Acceleration in g's:

Acceleration=24.9/9.8=2.54 g's