A disk turns through an angle of β(t)=Ct2 – Bt3 where C=3.20 rad/s2 and B= 0.500 rad/s3. Calculate the angular acceleration α(t) and velocit

Question

A disk turns through an angle of β(t)=Ct2 – Bt3 where C=3.20 rad/s2 and B= 0.500 rad/s3. Calculate the angular acceleration α(t) and velocity w(t) as a function of time.

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Khánh Gia 3 years 2021-08-14T04:49:59+00:00 1 Answers 7 views 0

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  1. sori
    0
    2021-08-14T04:51:54+00:00
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    Answer:

    ω(t) = 6.4 t – 1.5 t²

    α(t) = 6.4  – 3 t

    Explanation:

    The angular displacement of the disk is given as the function of time:

    β(t)=Ct² – B t³

    where,

    C = 3.2 rad/s²

    B = 0.5 rad/s³

    Therefore,

    β(t) = 3.2 t² – 0.5 t³

    Now, for angular velocity ω(t), we must take derivative of angular displacement with respect to t:

    ω(t) = dβ/dt = (d/dt)(3.2 t² – 0.5 t³)

    ω(t) = 6.4 t – 1.5 t²

    Now, for angular acceleration α(t), we must take derivative of angular velocity with respect to t:

    α(t) = dω/dt = (d/dt)(6.4 t – 1.5 t²)

    α(t) = 6.4  – 3 t

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