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.

Question

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)

jukilo · Answer

Apply conservation of energy as there is no friction.

Geoff · Answer

Would i take it from the center of mass?

fima · Answer

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?