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. part A What is the radial acceleration (in m/s^2 ) of the endolymph fluid? part B What is the radial acceleration (in g's) of the endolymph fluid? 2-A model of a helicopter rotor has four blades, each of length 4.00m from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 540rev/min . A-What is the linear speed of the blade tip? B-What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravity, g?

Answer 1

1)

Answer:

`a = 18.68 m/s^2`

Part b)

`a = 1.9 g`

Step-by-step explanation:

Rate of the spinning of the dancer is given as

`f = 2.6 rev/s`

angular speed is given as

`\omega = 2\pi f`

`\omega = 2\pi(2.6) = 16.33 rad/s`

distance of the ear is given as

`r = 7 cm = 0.07 m`

Part a)

Radial acceleration is given as

`a = \omega^2 r`

`a = (16.33)^2(0.07)`

`a = 18.68 m/s^2`

Part b)

also we know that

`g = 9.81 m/s`

so now we have

`(a)/(g) = (18.68)/(9.81)`

`a = 1.9 g`

2)

Answer:

Part a)

`v = 226.2 m/s`

Part b)

`a = 1.304 * 10^3 g`

Step-by-step explanation:

Length of the blades = 4.00 m

frequency of the blades = 540 rev/min

`f = 540 * (1)/(60) = 9 rev/s`

so angular speed is given as

`\omega = 2\pi f`

`\omega = 2\pi(9) = 56.5 rad/s`

Part a)

Linear speed of the tip of the blade is given as

`v = r\omega`

`v = (4.00)(56.5)`

`v = 226.2 m/s`

Part b)

Radial acceleration of the tip of the blade

`a = (v^2)/(r)`

`a = (226.2^2)/(4)`

`a = 1.28 * 10^4 m/s^2`

also we know

`(a)/(g) = (1.28 * 10^4)/(9.81)`

`a = 1.304 * 10^3 g`