BIO Dizziness.? 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?
Solution 24E The radial acceleration in a circular motion is given by 2 a r r ….(1) Here is the angular velocity and r is the radius of the circular path. Step 1 In the given problem we have = 3.0 revolution/s Now we know that 1 revolution = 2 rad angular rotation. Now putting this value in the above equation we have 2 rad = (3.0 revolution/s)( 1 revolution 6 rad/s And the radius of the circular path is r = 7.0 cm = 7.0 × 10 2 m Step 2 Now putting this value in the equation (1) we have 2 2 2 a r (6 rad/s) (7.0 × 10 m) = 1.3 m/s So the radial acceleration of the endolymph liquid is 1.3 ms .-2