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A ruler stands vertically against a wall. It is given a tiny impulse at θ=0∘ such that it starts falling down under the influence of gravity. You can consider that the initial angular velocity is very small so that ω(θ=0∘)=0. The ruler has mass m= 200 g and length l= 20 cm. Use g=10 m/s2 for the gravitational acceleration, and the ruler has a uniform mass distribution. Note that there is no friction whatsoever in this problem. (See figure)

(a) What is the angular speed of the ruler ω when it is at an angle θ=30∘? (in radians/sec)


(b) What is the force exerted by the wall on the ruler when it is at an angle θ=30∘? Express your answer as the x component Fx and the y component Fy (in Newton)



(c) At what angle θ0 will the falling ruler lose contact with the wall? (0≤θ0≤90∘; in degrees) [hint: the ruler loses contact with the wall when the force exerted by the wall on the ruler vanishes.]



    apply conservation of energy:
    EK= 1/2*I*w^2, I=1/3*m*L^2

    Eini= mg(L/2) + 0
    Efin= mg(L/2)cos30 + 1/2*I*w^2
    solve for Eini=Efin -> w=

    any one knows how to aswer the other questions?


    did this work for you? are you sure that we shouldn't use parallel axis theorem to find I? Because rod is rotating about end. And you assume that it's a point mass in the rotational motion.


    I don't think so.
    omega comes out too low

    I think part a) has to be done with energy conservation
    U at the top - U at 30° = K of rod


    the equation is Ok, and the w value got green checked. So YES, I'm sure about A.
    And I did for conservation of energy.

    But anyone knows how to do B and C. And please, try to post the procedure, because we all have different data.


    Can you guys help me with questions 2 and 3 ? I just have one more try but i am really confused in this two ;(

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