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)

Question

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

ω=

(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)

Fx=

Fy=

(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.]

θ0=

Answer 1

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?

Answer 2

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.

Answer 3

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

Answer 4

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.

Answer 5

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