Angular Velocity from Potential and Mechanical Energy of rotating rod

In summary, the conversation discusses finding the angular velocity of a falling rod when it meets the horizontal using equations for potential and mechanical energy. The correct method is to use the potential energy of the rod at the center of mass and equate it to the mechanical energy at the point of meeting the horizontal. The equation for initial potential energy should not include the (1/2) term.
  • #1
jstep
11
0

Homework Statement



I am asked to find the angular velocity of a falling rod in the instant that the rod meets the horizontal. The system is set up in this image:

1sdszo.jpg


The only force acting on the rod is gravity

Homework Equations



U = (1/2)MgL
K = (1/2)Iw2
Kf + Uf = Ki + Ui

The Attempt at a Solution



Can I solve this by using the potential energy of the rod with this equation:

U = (1/2)MgL

and then equating that to the Mechanical Energy at the point that it meets the horizontal?

I know the moment of inertia of the rod so if I do (1/2)MgL = (1/2)Iw2 and solve for omega, is that correct?

Also, when finding the initial potential energy, should i use the full length of the rod or only the length to the center of mass?

Thank you!
 
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  • #2
yes, you are correct. to calculate the initial potential energy, just use the altitude of the center of mass and drop the (1/2), that should not be there.

good luck
 
  • #3
Oh okay, so let me just make sure I understand:

so this is the correct way to find the initial potential energy?

U = mgLsin[tex]\theta[/tex]

where L is the length to the center of mass
 
  • #4
correct.
 
  • #5
thanks so much!
 

1. What is Angular Velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point. It is usually represented by the symbol ω (omega) and is measured in radians per second.

2. How is Angular Velocity related to Potential and Mechanical Energy?

Angular velocity is related to potential and mechanical energy through the conservation of energy principle. In a rotating system, the potential energy is converted into mechanical energy, which is then related to the angular velocity of the system.

3. How do you calculate Angular Velocity from Potential and Mechanical Energy?

To calculate angular velocity from potential and mechanical energy, you can use the formula ω = √(2E/I), where ω is the angular velocity, E is the mechanical energy, and I is the moment of inertia of the rotating object.

4. What is the importance of understanding Angular Velocity from Potential and Mechanical Energy?

Understanding angular velocity from potential and mechanical energy is important in many fields of science and engineering, such as in the study of rotating systems, celestial mechanics, and even in the design of machinery and vehicles.

5. Can Angular Velocity be changed by altering the Potential or Mechanical Energy?

Yes, angular velocity can be changed by altering the potential or mechanical energy of a rotating system. For example, increasing the potential energy of an object will result in an increase in its angular velocity, while decreasing the mechanical energy will cause a decrease in the angular velocity.

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