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College Physics

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A child swings a yo-yo of weight mg in a horizontal circle so that the cord makes an angle of 30 degrees with the vertical. Find the centripetal acceleration.

  • College Physics -

    Ok, the radius of rotation is length*sin30 where length is the length of string.

    looking at vectors, mg is down, and mv^2/r is outward, so tan30=mv^2/(r*mg)

    tan 30= v^2/(length*sin30*g)

    but v= 2PI(length*sin30) square that, put it in the equation

    tan30=4PI^2*length*sin30/g check that. solve for length of string.

    finally, centacc= v^2/r and you can do that algebra.

  • College Physics -

    You did not say what the mass M is. As turns out, you don't need to know M to get the answer. First convert the mass to weight, W.
    W = Mg
    The vertical component of string tension is T cos30 = Mg
    The horizontal component of string tension is the centripetal force
    T sin30 = Ma,
    where a is the centripetal acceleration

    Divide one by the other and you get
    sin30/cos30 = tan30 = sqrt3 = a/g

    Solve for a.

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