An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11.0 m and, in starting, rotates according to θ = 0.260t2, wher

Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11.0 m and, in starting, rotates according to θ = 0.260t2, where t is in seconds and θ is in radians. When t = 2.40 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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Kim Chi 5 years 2021-09-05T08:46:28+00:00 1 Answers 10 views 0

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  1. thuhuong
    0
    2021-09-05T08:48:25+00:00
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    Answer:

    a) 1.248 rad/s

    b) 13.728 m/s

    c) 0.52 rad/s^2

    d) 17.132m/s^2

    Explanation:

    You have that the angles described by a astronaut is given by:

    \theta=0.260t^2

    (a) To find the angular velocity of the astronaut you use the derivative og the angle respect to time:

    \omega=\frac{d\theta}{dt}=\frac{d}{dt}[0.260t^2]=0.52t

    Then, you evaluate for t=2.40 s:

    \omega=0.52(2.40)=1.248\frac{rad}{s}

    (b) The linear velocity is calculated by using the following formula:

    v=\omega r

    r: radius if the trajectory of the astronaut = 11.0m

    You replace r and w and obtain:

    v=(1.248\frac{rad}{s})(11.0m)=13.728\frac{m}{s}

    (c) The tangential acceleration is:

    a_T=\alpha r\\\\\alpha=\frac{\omega^2}{2\theta}=\frac{(1.248rad/s)^2}{2(0.260(2.40s)^2)}=0.52\frac{rad}{s^2}

    (d) The radial acceleration is:

    a_r=\frac{v^2}{r}=\frac{(13.728m/s)^2}{11.0m}=17.132\frac{m}{s^2}

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