Calculating Speed and Kinetic Energy in a Rotating Rod

In summary, the conversation discusses the problem of a thin rod of uniform mass distribution pivoted at one end and swinging down to the vertical position. The mass and length of the rod are given and the problem asks for the speed of its center of gravity at its lowest position and the tangential speed at the free end of the rod. The relevant equations for moment of inertia and tangential acceleration are provided. The attempt at a solution involved using the formula for potential and kinetic energy, but the answer was incorrect. The conversation then delves into the units and type of kinetic energy involved in the problem.
  • #1
tamakitty
1
0

Homework Statement


[/B]
The diagram shows a thin rod of uniform mass distribution pivoted about one end by a pin passing through that point. The mass of the rod is 0.380 kg and its length is 2.50 m. When the rod is released from its horizontal position, it swings down to the vertical position as shown.

(a) Determine the speed of its center of gravity at its lowest position.

(b) When the rod reaches the vertical position, calculate the tangential speed of the free end of the rod.

Homework Equations



Moment of Inertia for a solid rod: 1/3MR^2

Tangential Acceleration = r * (dω/dt)

The Attempt at a Solution



I really doubt this is right, but this is what I have been trying.

For part A, this is what I did.
To get the center of mass, I tried 2.5/2 for 1.25.
For the speed at that point, I tried using mgh for potential/kinetic energy and got (0.38g)(9.81m/s^2)(1.25). This gave me 4.66. Then I square rooted 4.66 over 0.38 (the mass), and got 4.95.

My answer was incorrect

For part B, I assumed that it was the answer for part A multiplied by two, since A was asking for the center, rather than the full rod. I'll need to figure out part A before part B.
 
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  • #2
tamakitty said:
I really doubt this is right, but this is what I have been trying.

For part A, this is what I did.
To get the center of mass, I tried 2.5/2 for 1.25.
For the speed at that point, I tried using mgh for potential/kinetic energy and got (0.38g)(9.81m/s^2)(1.25). This gave me 4.66. Then I square rooted 4.66 over 0.38 (the mass), and got 4.95.

My answer was incorrect
You should always show the units for the values you calculate. For example, what units are associated with the 4.66 value?

Since the mass was not falling linearly but rotationally, what form of kinetic energy is involved? What's an expression for it?
 

1. How does the length of the swinging rod affect its rotation?

The length of the swinging rod has a direct impact on its rotation. According to the law of conservation of angular momentum, a longer rod will have a slower rotation compared to a shorter rod with the same mass and velocity. This is because the longer rod has a greater moment of inertia, making it harder to rotate.

2. Does the mass of the swinging rod affect its rotation?

Yes, the mass of the swinging rod also plays a role in its rotation. An object with a greater mass will have a greater moment of inertia and therefore will require more force to rotate at a certain velocity. This means that a heavier rod will have a slower rotation compared to a lighter rod with the same length and velocity.

3. How does the angle of release affect the rotation of the swinging rod?

The angle of release can have a significant impact on the rotation of a swinging rod. The higher the angle of release, the greater the initial velocity of the rod and therefore the faster the rotation. However, if the angle is too high, the rod may not have enough time to rotate fully and may fall back in the opposite direction.

4. Can the rotation of a swinging rod be affected by external factors?

Yes, the rotation of a swinging rod can be affected by external factors such as air resistance and friction. These forces can slow down the rotation of the rod and may even cause it to stop completely. In a vacuum, where there is no air resistance or friction, the rod would continue to rotate indefinitely.

5. How does the gravitational force impact the rotation of a swinging rod?

The gravitational force also plays a role in the rotation of a swinging rod. As the rod swings, it experiences a downward force due to gravity which can affect its rotation. Depending on the length and mass of the rod, the gravitational force may either speed up or slow down its rotation. In a vacuum, where there is no gravity, the rod would continue to rotate at a constant velocity.

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