At a certain instant a rigid wheel is spinning about its center of mass with angular velocity of magnitude ω and angular acceleration of mag

Question

At a certain instant a rigid wheel is spinning about its center of mass with angular velocity of magnitude ω and angular acceleration of magnitude α. Consider a point a distance r from the axis of rotation. What would be the magnitude of the acceleration of this point on the wheel?

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Latifah 5 years 2021-08-28T19:10:51+00:00 1 Answers 44 views 0

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  1. Bo
    0
    2021-08-28T19:12:00+00:00
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    Answer:

    a = r√(w⁴ + (alpha)²)

    Explanation:

    let w be the magnitude of angular velocity

    r = radius

    v = velocity = wr

    angular acceleration, ā = v²/r = (wr)²/r = w²r

    Also,

    â = dv/dt = rdw/dt

    given : alpha = dw/dt

    hence, â = (alpha)r

    the resultant acceleration, a, by Pythagoras is given as

    a = √( â² + ā²) = √(r²w⁴ + r²(alpha)²)

    simplifying,

    a = √r²(w⁴ + (alpha)²)

    a = r√(w⁴ + (alpha)²)

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