What Is the Angular Speed of a Falling Ruler at 30 Degrees?

[Ruitker]

Homework Statement

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)

The angle is from the vertical.

Homework Equations

I'm not sure on which method to use. I was thinking either conservation of energy or using the centre of mass equations.

The Attempt at a Solution

Various attempts that have not yielded correct answers.

 

[HallsofIvy]

Personally, I wouldn't use either "conservation of energy" or "center of mass". I would apply the equations of motion to the end of the ruler. You know that the downward acceleration is always "-g" (-9.82 m/s^2). But the rule cannot fall straight because the ruler is "rigid". So separate the vector <0, -g> into one component along the length of the ruler and one at right angles to the ruler at each angle. Only the perpendicular component acts accelerates the end of the ruler.

 

[Ruitker]

Personally, I wouldn't use either "conservation of energy" or "center of mass". I would apply the equations of motion to the end of the ruler. You know that the downward acceleration is always "-g" (-9.82 m/s^2). But the rule cannot fall straight because the ruler is "rigid". So separate the vector <0, -g> into one component along the length of the ruler and one at right angles to the ruler at each angle. Only the perpendicular component acts accelerates the end of the ruler.

Thanks for your suggestions. I am not sure i understand what you mean. Shall i calculate the velocity and then convert to angular velocity or is there a trick i am missing.

 

[Tanero]

I would apply the equations of motion to the end of the ruler.

Isn't it better to write equation of motion for center of mass?
We need to find ω(θ) relationship. And to do this. Well, I am stuck too with this problem.