You are sitting on a merry-go-round at a distance of 2m from its center. It spins 15 times in 3 min. What distance do you move as you make o

Question

You are sitting on a merry-go-round at a distance of 2m from its center. It spins 15 times in 3 min. What distance do you move as you make one revolution? What is your angular speed in RPM? What is your linear speed in meters per SECOND?

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MichaelMet 2 weeks 2021-09-02T09:38:35+00:00 1 Answers 0 views 0

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    2021-09-02T09:39:42+00:00

    Answer:

    A) 12.57 m

    B) 5 RPM

    C) 3.142 m/s

    Explanation:

    A) Distance covered in 1 Revolution:

    The formula that gives the relationship between the arc length or distance covered during circular motion to the angle subtended or the revolutions, is given as follows:

    s = rθ

    where,

    s = distance covered = ?

    r = radius of circle = 2 m

    θ = Angle = 2π radians  (For 1 complete Revolution)

    Therefore,

    s = (2 m)(2π radians)

    s = 12.57 m

    B) Angular Speed:

    The formula for angular speed is given as:

    ω = θ/t

    where,

    ω = angular speed = ?

    θ = angular distance covered = 15 revolutions

    t = time taken = 3 min

    Therefore,

    ω = 15 rev/3 min

    ω = 5 RPM

    C) Linear Speed:

    The formula that gives the the linear speed of an object moving in a circular path is given as:

    v = rω

    where,

    v = linear speed = ?

    r = radius = 2 m

    ω = Angular Speed in rad/s = (15 rev/min)(2π rad/1 rev)(1 min/60 s) = 1.571 rad/s

    Therefore,

    v = (2 m)(1.571 rad/s)

    v = 3.142 m/s

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