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12 May, 01:21

A child is riding a merry-go-round, which has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s 2. The child is standing 4.65 m from the center of the merrygo-round.

What is the magnitude of the acceleration of the child?

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  1. 12 May, 03:38
    0
    8.05 m/s^2

    Explanation:

    Instantaneous angular speed (w) = 1.25 rad/s

    Angular acceleration (α) = 0.745 rad/s^2

    Distance from the centre to where the child is (r) = 4.65m

    Tangential acceleration = αr

    = 0.745 * 4.65

    = 3.464 m/s^2

    Centripetal acceleration = w^2r

    = (1.25) ^2 (4.65)

    = 7.266 m/s^2

    Total acceleration = √3.464^2 + 7.266^2

    = √64.794052

    = 8.05m/s^2
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