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An astronaut is being tested in a centrifuge. The centrifuge has a radius R and, in starting, rotates according to θ = tn, where t is in seconds, θ is in radians, and n is a positive integer. Find expressions for the the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration at a general time t, in terms of the variables given.

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Answer:

a) ω=n

b) V = R*n

c) a = 0

d) [tex]ar = R*n^2[/tex]

Explanation:

Angular velocity is given by the derivative of θ:

ω = n

Linear Velocity will be:

V = ω*R = n*R

Tangential acceleration will be the derivative of the linear velocity. Since velovity is constant:

a = 0

Radial acceleration is given by:

[tex]ar = V^2/R = (R*n)^2/R=R*n^2[/tex]

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