A motorcycle, which has an initial linear speed of 7.8 m/s, decelerates to a speed of 1.4 m/s in 5.8 s. Each wheel has a radius of 0.67 m an

Question

A motorcycle, which has an initial linear speed of 7.8 m/s, decelerates to a speed of 1.4 m/s in 5.8 s. Each wheel has a radius of 0.67 m and is rotating in a counterclockwise (positive) directions. What is (a) the constant angular acceleration (in rad/s2) and (b) the angular displacement (in rad) of each wheel

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niczorrrr 5 years 2021-08-15T18:12:04+00:00 1 Answers 471 views 0

Answers ( )

  1. Maris
    0
    2021-08-15T18:13:41+00:00
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    Answer:

    (a) 1.64 rad/s²

    (b) 39.94 rad

    Explanation:

    (a) From the question,

    α = a/r……………. Equation 1

    Where a = linear acceleration if the motorcycle wheel, r = radius of the wheel, α = angular velocity of the wheel.

    But,

    a = (v-u)/t………….. Equation 2

    Given: v = 1.4 m/s, u = 7.8 m/s, t = 5.8 s

    Substitute into equation 2.

    a = (1.4-7.8)/5.8

    a = -1.1 m/s².

    Note: The negative sign shows that the motorcycle is decelerating

    Also given: r = 0.67 m.

    Substitute into equation 1

    α = 1.1/0.67

    α  = 1.64 rad/s²

    (b)

    Θ = s/r………………. Equation 3

    Where s = linear displacement, Θ = angular displacement.

    But,

    s = (v²-u²)/2a………. Equation 2

    s = (1.4²-7.8²)/[2×(-1.1)]

    s = -58.88/-2.2

    s = 26.76 m.

    therefore,

    Θ = 26.76/0.67

    Θ = 39.94 rad.

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