Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness. (a) If a human centrifuge has a radius of 4.87 m, what angular speed (in rad/s) results in a centripetal acceleration of 9g? rad/s= (b) What linear speed (in m/s) would a person in the centrifuge have at this acceleration? m/s=
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
(a) centrifugal acceleration is given by,
where is angular speed
R is radius
Here, = 9g=88.2 m/s2
R= 4.87 m
So, we can write
88.2 m/s2 = x 4.87m
= (88.2/4.87) rad2/s2 = 18.11 rad2/s2
= rad/s = 4.256 rad /s = 4.26 rad/s
So, angular speed is 4.26 rad/s .
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