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Rotational Motion Physics Problem

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A car starts from rest on a curve with a radius of 150 and accelerates at 1.2.Through what angle will the car have traveled when the magnitude of its total acceleration is 2.2 ?

  • Rotational Motion Physics Problem -

    Given:R=150m,
    tangential component of acceleration a(τ)=1.2 m/s²,
    a=2.2 m/s²,
    φ=?
    a²=a(n)²+a(τ)²,
    where a(n) is the normal( centripetal) component of acceleration.
    a(n)= sqrt(a²-a(τ)²) = sqrt(2.2²-1.2²) = 1.84 m/s²
    a(n)=ω²•R =>
    ω² = a(n)/R
    The angular acceleration ε= a(τ)/R.
    From
    φ=ε•t²/2
    ω=ε•t,
    we obtain
    φ=ω²/2•ε= a(n)/2•a(τ)=
    =1.84/2•1.2=0.77 rad.

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