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= 100 g and length l= 35 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)

ω=

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(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=

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Fy=

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(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=

yes please.. that's the only question where I'm stuck too..

Me too!!!

Hi Teresa, can you do rocket problem me pls?

p: percentage (4.5% is burned in 155s)

m:mass of rocket
u:fuelspeed in meter/s!

v=u*ln(1/(1-p))=1500*ln(1/0.955)

a=v/t = 69.065/155= 0.4455

Hi Teresa, in my problem, question says The rocket burns 10 % of its mass in 290 s (assume the burn rate is constant).

What is the speed of the rocket after a burn time of 145.0 s?

How did you find 4.5% is burned in 155 sec? Pls.
Thank you very much

because they ask you for half of the time,

so in your case in 145 it gets burned 5% in 145 seconds

Thank you very much Teresa. I got green check. Now time for rular one..

in the equation above what is the "ln"?

"ln" is like log..it is in your calculator

is the "u" the ejected fuel in m/s instead of km/s?