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21 April, 22:37

A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.46 rad/s2. How many revolutions does the wheel make during this time?

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Answers (2)
  1. 21 April, 23:49
    0
    3.025 revolutions

    Explanation:

    To solve this question firstly we need to calculate the time t

    Given the angular velocity and the angular acceleration

    The time t = angular velocity/angular acceleration

    Converting 50rpm to rad/s

    = 50 * 2π / 60

    =1.67 rad/s

    t = 1.67/0.46

    t = 3.63s

    The wheel makes 50 revolutions in one minute

    Therefore in 3.63s, it will make

    3.63 * 50/60

    = 181.5/60

    =3.025 revolutions

    Approximately 3 revolutions
  2. 22 April, 01:34
    0
    A. 9.84 rad/sec or

    = 93.93 rev/min

    B. 12 turns.

    Explanation:

    ωf = ω° + αt

    Where,

    t = 10s

    ω° = initial speed in rad / s

    = 50 rev/min (rpm)

    Converting rpm to rad/sec,

    50 * 2π/60

    = 5.236 rad/s

    α = angular acceleration = 0.46 rad/s^2

    ωf = final angular velocity

    ωf = 5.236 + 0.46*10sec

    ωf = 9.84 rad/sec or

    = 93.93 rev/min

    B.

    θ = ω°*t + 1/2 * (α*t^2)

    Where,

    θ = angular displacement in rad.

    θ = 5.236 * 10 + 0.5 * 0.46 * (10) ^2

    = 52.36 + 23

    = 75.36 rad n turns

    = 75.36/2π

    = 12 turns
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