An automobile accelerates from zero to 30 m/s in 6 s. The wheels have a diameter of 0.4 m. What is the angular acceleration of each wheel

Question

An automobile accelerates from zero to 30 m/s in 6 s. The wheels have a diameter of 0.4 m. What is the angular acceleration of each wheel

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Kim Chi 4 years 2021-08-19T00:16:35+00:00 1 Answers 9 views 0

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  1. vankhanh
    0
    2021-08-19T00:18:12+00:00
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    Answer:

    12.5 rad/s²

    Explanation:

    Angular Acceleration: This can be defined as the ratio of linear acceleration and radius. The S.I unit is rad/s²

    From the question,

    a = αr………………. Equation 1

    Where a = linear acceleration, α = angular acceleration, r = radius.

    But,

    a = (v-u)/t………….. Equation 2

    Where v = final velocity, u = initial velocity, t = time.

    Substitute equation 2 into equation 1

    (v-u)/t = αr

    make α the subject of the equation

    α = (v-u)/tr…………….. Equation 3

    Given: v = 30 m/s, u = 0 m/s, t = 6 s, r = 0.4 m

    Substitute into equation 3

    α = (30-0)/(0.4×6)

    α = 30/2.4

    α = 12.5 rad/s²

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