A disk of radius 25 cm spinning at a rate of 30 rpm slows to a stop over 3 seconds. What is the angular acceleration? B. How many radia

Question

A disk of radius 25 cm spinning at a rate of 30 rpm slows to a stop over 3 seconds. What is the angular acceleration?
B. How many radians did the disk turn while stopping ?
C. how many revolutions?

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Thạch Thảo 5 months 2021-08-30T14:04:58+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-08-30T14:06:45+00:00

    Answer:

    A. α = – 1.047 rad/s²

    B. θ = 14.1 rad

    C. θ = 2.24 rev

    Explanation:

    A.

    We can use the first equation of motion to find the acceleration:

    \omega_f = \omega_i + \alpha t\\

    where,

    ωf = final angular speed = 0 rad/s

    ωi = initial angular speed = (30 rpm)(2π rad/1 rev)(1 min/60 s) = 3.14 rad/s

    t = time = 3 s

    α = angular acceleration = ?

    Therefore,

    0\ rad/s = 3.14\ rad/s + \alpha (3\ s)\\

    α = – 1.047 rad/s²

    B.

    We can use the second equation of motion to find the angular distance:

    \theta = \omega_i t + \frac{1}{2}\alpha t^2\\\theta = (3.14\ rad/s)(3\ s) + \frac{1}{2}(1.04\ rad/s^2)(3\ s)^2\\

    θ = 14.1 rad

    C.

    θ = (14.1 rad)(1 rev/2π rad)

    θ = 2.24 rev

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