An astronaut is being tested in a centrifuge. The centrifuge has a radius of 7.40 m and, in starting, rotates according to θ = 0.190t2, where t is in seconds and θ is in radians. When t = 3.60 s, what are the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration?
Angular displacement of the astronaut is given by,
(t) = 0.19t2
If we differentiate the equation of angular displacement with respect to time we will get the equation for angular velocity,
(t) = 0.38t
If we differentiate the equation of angular velocity with respect to time we will get the equation for angular acceleration,
(t) = 0.38
Radius of the centrifuge = R = 7.4 m
Angular velocity at t=3.6 sec = 1 = (0.38)(3.6) = 1.368 rad/s
Angular acceleration at t=3.6 sec = 1 = 0.38 rad/s2
Linear velocity of the astronaut at t=3.6 sec = V1
V1 = 1R
V1 = (1.368)(7.4)
V1 = 10.12 m/s
Tangential acceleration of the astronaut at t=3.6 sec = at1
at1 = 1R
at1 = (0.38)(7.4)
at1 = 2.812 m/s2
Radial acceleration of the astronaut at t=3.6 sec = ar1
ar1 = 12R
ar1 = (1.368)2(7.4)
ar1 = 13.85 m/s2
a) Magnitude of astronaut's angular velocity at t=3.6 sec = 1.368 rad/s
b) Magnitude of astronaut's linear velocity at t=3.6 sec = 10.12 m/s
c) Magnitude of astronaut's tangential acceleration at t=3.6 sec = 2.812 m/s2
d) Magnitude of astronaut's radial acceleration at t=3.6 sec = 13.85 m/s2
An astronaut is being tested in a centrifuge. The centrifuge has a radius of 7.40 m...
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