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31 January, 09:54

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 5.20 m and, in starting, rotates according to θ = 0.170t2, where t is in seconds and θ is in radians. When t = 4.70 s, what are the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration?

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  1. 31 January, 10:21
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    A) angular velocity; ω = 1.598 rad/s

    B) linear velocity; V = 8.31 m/s

    C) Tangential Acceleration; a_t = 1.768 m/s²

    D) Radial Acceleration; a_r = 13.28 m/s²

    Explanation:

    We are given that;

    Radius; r = 5.2m

    Time; t = 4.7 sec

    θ = 0.170t²

    Thus, angular acceleration would be the second derivative of θ which is d²θ/dt²

    Thus,α = d²θ/dt² = 0.34 rad/s²

    A) Formula for angular velocity is;

    ω = αt

    Where α is angular acceleration and t is time.

    Thus; ω = 0.34 x 4.7

    ω = 1.598 rad/s

    b) formula for linear velocity is given by; V = ωr

    We have ω = 1.598 rad/s and r = 5.2m

    Thus; V = 1.598 x 5.2

    V = 8.31 m/s

    c) formula for tangential acceleration is;

    a_t = αr

    a_t = 0.34 x 5.2

    a_t = 1.768 m/s²

    d) formula for radial acceleration is;

    a_r = rω²

    a_r = 5.2 x 1.598²

    a_r = 13.28 m/s²
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