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 2.7 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.

1.) What is the radical acceleration (in m/s^2) of the endolymph fluid?
a = ?
2.) What is the radical acceleration (in g's) of the endolymph fluid?
a = ?

1. 20.15 m/s² 2. 2.06g

Explanation:

The radial acceleration a = rω² where ω = angular speed and r = radius.

The angular speed of the dancer = 2.7 revolutions per second = 2.7 × 2π rad/s = 16.965 rad/s. The radius, r = distance from vertical axis of spin = 7.0 cm = 0.07 m.

So, a =  rω² = 0.07 × 16.965² m/s² = 20.146 m/s² ≅ 20.15 m/s²

2. The radial acceleration in g's.

a/g = 20.15/9.8 = 2.055 ≅ 2.06

So, a = 2.06g

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.

the right answer is 0.3 meters per second