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31 October, 00:43

The angular velocity of a flywheel obeys the equation ωz (t) = A+Bt2, where t is in seconds and A and B are constants having numerical values 2.65 (for A) and 1.60 (for B).

Required:

a. What are the units of A and B if ωz is in rad/s?

b. What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?

c. Through what angle does the flywheel turn during the first 2.00 s?

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Answers (1)
  1. 31 October, 04:04
    0
    a)

    Iz (t) = A + B t²

    Iz (t) = angular velocity

    putting dimensional formula

    T⁻¹ = A + Bt²

    A = T⁻¹

    unit of A is rad s⁻¹

    BT² = T⁻¹

    B = T⁻³

    unit of B is rad s⁻³

    b)

    Iz (t) = A + B t²

    dIz / dt = 2Bt

    angular acceleration = 2Bt

    at t = 0

    angular acceleration = 0

    at t = 5

    angular acceleration = 2 x 1.6 x 5

    = 16 rad / s²

    Iz (t) = A + B t²

    dθ / dt = A + B t²

    integrating,

    θ = At + B t³ / 3

    when t = 0, θ = 0

    when t = 2

    θ = At + B t³ / 3

    = 2.65 x 2 + 1.6 x 2³ / 3

    = 5.3 + 4.27

    = 9.57 rad.

    Flywheel turns by 9.57 rad during first 2 s.
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