Solve Angular Speed of Rotating Rod: Conservation of Energy

In summary, the author of the JPEG image forgot to take into account the torque's dependence on angle, and so the answer to the question is not constant.
  • #1
rasensuriken
10
0
The question is as the attachment...
May i know if i want to find the angular speed of the rod when it inclined at certain angle, or at horizontal, can i use the [tex]\varpi[/tex]^2=[tex]\varpi[/tex]_0^2+2[tex]\alpha[/tex][tex]\vartheta[/tex]?

Attempt: I used it, and used conservation of energy, the latter produces right answer, but i don't know why first one won't work. Any clues?
 

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    rotating.jpg
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  • #2
Hi rasensuriken! :smile:

I can't read your formula … but, looking at the .jpg, I don't think the angular acceleration, α, is constant (because the torque from the weight is different for different angles).

So a formula using constant α won't work! :smile:
 
  • #3
tiny-tim is right, the author of the JPEG image made a mistake. He forgot that the torque is a cross product of radius and the force, which depends on the angle. And the angle changes as the whole thing swings down, so the alpha should be more like:
[tex]\tau = MG\frac{L}{2} \sin{\omega t}[/tex]
Which, as you can see, depends on the time and so is not constant. The conservation of energy worked because it does not care about the acceleration at any point, but only on the initial and final conditions.
 
  • #4
Hi kkrizka! :smile:

No, he didn't forget … he only asked for the inital values, for which his equations are correct.

The question in the OP is rasensuriken boldly going further! :smile:
 
  • #5
tiny-tim said:
Hi kkrizka! :smile:

No, he didn't forget … he only asked for the inital values, for which his equations are correct.

The question in the OP is rasensuriken boldly going further! :smile:

Ah whoops, I've been reading too many phys problems lately and they are starting to get mixed up. :P
 
  • #6
ya...i also just thought of that...the acceleration is not constant...because the L/2 relative to the center of mass keep on changing...thanks!
 

1. What is angular speed?

Angular speed is a measure of how fast an object is rotating around a fixed point. It is measured in radians per second (rad/s) or revolutions per minute (RPM).

2. How do you calculate angular speed?

Angular speed can be calculated by dividing the angular displacement (change in angle) by the time it takes to make that change. The formula for angular speed is ω = Δθ/Δt, where ω is angular speed, Δθ is angular displacement, and Δt is time.

3. What is the conservation of energy?

The conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In other words, the total energy in a closed system remains constant.

4. How is conservation of energy related to the rotation of a rod?

In the context of a rotating rod, the conservation of energy means that the total energy of the system (which includes the kinetic energy of the rod and any potential energy associated with its position) remains constant as the rod rotates. This allows us to use the conservation of energy principle to solve for the angular speed of the rod.

5. What are the factors that affect the angular speed of a rotating rod?

The angular speed of a rotating rod can be affected by several factors, such as the mass and length of the rod, the force applied to it, and any external torque acting on it. Additionally, the conservation of energy principle tells us that the potential energy of the rod (due to its position) can also affect its angular speed.

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