Rotational Motion- Parallel Axis Theorem?

In summary, the problem involves a meter stick being held to a wall by a nail and released from an initial horizontal position to swing freely without friction. The parallel axis theorem is used to find the moment of inertia, which is 0.09. However, the next step of finding the angular velocity is unclear and may involve using the conservation of mechanical energy equation and determining the potential energy of the meter stick.
  • #1
elianaphys
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Homework Statement


A meter stick is held to a wall by a nail passing through the 60-cm mark. The meter stick is free to swing about this nail, without friction. If the meter stick is released from an initial horizontal position, what angular velocity will it attain when it swings through the vertical position?

Homework Equations


Parallel Axis theorem Iz=Icm+mr^2
Conservation of Mechanical Energy E=1/2Iω^2+U=[constant]

The Attempt at a Solution


By using the parallel axis theorem, I have found the moment of Inertia, which is 0.09. Now, I am a bit stuck as to how to apply this toward finding the angular velocity. I believe rotational kinetic energy is a necessary intermediary step, but I am unsure about how to get there.

FYI, I am doing this through an online course and so have myself and a textbook--no teacher. I sincerely appreciate any and all help!
 
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  • #2
elianaphys said:

Homework Statement


A meter stick is held to a wall by a nail passing through the 60-cm mark. The meter stick is free to swing about this nail, without friction. If the meter stick is released from an initial horizontal position, what angular velocity will it attain when it swings through the vertical position?

Homework Equations


Parallel Axis theorem Iz=Icm+mr^2
Conservation of Mechanical Energy E=1/2Iω^2+U=[constant]

The Attempt at a Solution


By using the parallel axis theorem, I have found the moment of Inertia, which is 0.09. Now, I am a bit stuck as to how to apply this toward finding the angular velocity. I believe rotational kinetic energy is a necessary intermediary step, but I am unsure about how to get there.

FYI, I am doing this through an online course and so have myself and a textbook--no teacher. I sincerely appreciate any and all help!
How is potential energy determined for the meter stick ?
 

Related to Rotational Motion- Parallel Axis Theorem?

1. What is the Parallel Axis Theorem for rotational motion?

The Parallel Axis Theorem states that the moment of inertia of a rigid body about an axis parallel to the body's center of mass is equal to the moment of inertia about the center of mass plus the mass of the body multiplied by the square of the distance between the two axes.

2. How is the Parallel Axis Theorem used in rotational motion calculations?

The Parallel Axis Theorem is used to calculate the moment of inertia of a rigid body when it is rotating about an axis that is not passing through its center of mass. It allows us to shift the axis of rotation to a more convenient location, making the calculation easier.

3. What is the difference between the Parallel Axis Theorem and the Perpendicular Axis Theorem?

The Parallel Axis Theorem and the Perpendicular Axis Theorem are both used to calculate the moment of inertia of a rigid body. The difference is that the Parallel Axis Theorem is used for rotation about an axis parallel to the body's center of mass, while the Perpendicular Axis Theorem is used for rotation about an axis perpendicular to the body's plane of symmetry.

4. Can the Parallel Axis Theorem be applied to all types of rigid bodies?

Yes, the Parallel Axis Theorem can be applied to all types of rigid bodies, as long as they have a well-defined center of mass and a known mass distribution. It is commonly used in problems involving solid objects such as disks, cylinders, and spheres.

5. Is the Parallel Axis Theorem only applicable to rotational motion in a two-dimensional plane?

No, the Parallel Axis Theorem can be applied to three-dimensional rotational motion as well. It is valid for any axis of rotation that is parallel to the body's center of mass, regardless of the plane in which the rotation occurs.

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