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26 August, 17:38

During a tennis serve, a racket is given an angular acceleration of magnitude 150 rad/s^2. At the top of the serve, the racket has an angular speed of 12.0 rad/s. If the distance between the top of the racket and the shoulder is 1.30 m, find the magnitude of the total acceleration of the top of the racket.

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  1. 26 August, 18:00
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    270 m/s²

    Explanation:

    Given:

    α = 150 rad/s²

    ω = 12.0 rad/s

    r = 1.30 m

    Find:

    a

    The acceleration will have two components: a radial component and a tangential component.

    The tangential component is:

    at = αr

    at = (150 rad/s²) (1.30 m)

    at = 195 m/s²

    The radial component is:

    ar = v² / r

    ar = ω² r

    ar = (12.0 rad/s) ² (1.30 m)

    ar = 187.2 m/s²

    So the magnitude of the total acceleration is:

    a² = at² + ar²

    a² = (195 m/s²) ² + (187.2 m/s²) ²

    a = 270 m/s²
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