Physics

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= 250 g and length l= 25 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.

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

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  1. Apply conservation of energy as there is no friction.

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  2. Would i take it from the center of mass?

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  3. apply conservation of energy:
    U=m*g*hcm
    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?

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