Why is my calculation for the speed of a falling rod off by sqrt(2)?

No problem!In summary, a thin uniform rod of mass M and length L is positioned vertically above an anchored frictionless pivot point and then allowed to fall to the ground. The speed of the free end of the rod as it strikes the ground can be calculated using the equation mg(0.5L) = 0.5I\omega^2, with the moment of inertia being 1/3mL^2 for a stick rotating about the end. However, the calculated answer may be off by sqrt(2) from the correct answer, sqrt(3gL), due to the center of mass changing a distance of L/2.
  • #1
faculaganymede
3
0
A thin uniform rod of mass M and length L is positioned vertically above an anchored frictionless pivot point and then allowed to fall to the ground. With what speed does the free end of the rod strike the ground?
My answer is off by sqrt(2) from the correct answer, sqrt(3gL), and I don't understand why. Please help!
 
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  • #2
the gpe is being transformed into KE rotational. you would use the height as L/2 since the center of mass is changing that much distance.
the moment of inertia of a stick rotating about the end is 1/3mL^2

[tex] mg(0.5L) = 0.5I\omega^2 [/tex]
 
  • #3
faculaganymede said:
A thin uniform rod of mass M and length L is positioned vertically above an anchored frictionless pivot point and then allowed to fall to the ground. With what speed does the free end of the rod strike the ground?
My answer is off by sqrt(2) from the correct answer, sqrt(3gL), and I don't understand why. Please help!

You should not have posted this here. Did you not read https://www.physicsforums.com/showthread.php?t=89899 thread ?


regards
marlon
 
  • #4
sorry, that was my first post. didn't know better.
 
  • #5
Thanks Andrew!
 

FAQ: Why is my calculation for the speed of a falling rod off by sqrt(2)?

1. What is torque?

Torque is the measure of a force's tendency to cause an object to rotate around an axis or pivot point. It is represented by the symbol "τ" and is calculated by multiplying the force applied by the distance from the axis of rotation.

2. How does torque affect rotational motion?

Torque causes an object to rotate, either speeding it up or slowing it down depending on the direction of the force. The greater the torque applied, the faster the object will rotate, and the smaller the torque, the slower the rotation will be.

3. What is inertia?

Inertia is the resistance of an object to change its state of motion. It is directly related to the mass of an object, with more massive objects having greater inertia. Inertia can be thought of as the tendency of an object to keep moving in the same direction and at the same speed unless acted upon by an external force.

4. How does inertia relate to torque?

Inertia and torque are directly related. The greater the inertia of an object, the more torque is needed to change its rotational motion. This is why it is easier to rotate a less massive object than a more massive one.

5. How do torque and inertia affect everyday objects?

Torque and inertia play a significant role in our everyday lives. For example, when riding a bike, applying torque to the pedals causes the wheels to rotate, and the bike to move forward. Inertia also allows us to stay upright while riding, as our bodies resist changes in motion. In everyday objects, torque and inertia are essential for understanding how they move and function.

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