Calculating moment of inertia

In summary, the conversation discusses the calculation of the moment of inertia of a wheel using the falling mass method. This involves using measurements of the distance and time to determine the acceleration of the falling mass, which can then be used to calculate the rotational inertia of the wheel. The equation \tau = I \alpha is used to find the rotational inertia, and the conversation also mentions the use of Newton's 2nd law and torque calculations.
  • #1
Could anyone help me calculate the moment of inertia of a wheel by the falling mass method, the data I've got is below,

Distance mass falls

Time taken

Mass fallen

Radius of shaft that the wire wraps around which is attached to the mass

Is is just the mass*radius^2? It just doesn't seem right?

Thanks
 
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  • #2
I assume you have a light cable wrapped around the wheel shaft with a mass at the end. Then you let the mass fall from rest? And that the purpose of the experiment is to determine the rotational inertia of the wheel?

Given the acceleration of the falling mass you can figure out the rotational inertia of the wheel. You can figure out the acceleration from measurements of the time and distance (using kinematics).

To see how the rotational inertia relates to the acceleration of the falling mass, apply Newton's 2nd law to the wheel and to the falling mass.
 
  • #3
Yes the wire is deemed of no mass and the mass added falls from rest, I've calculated the acceleration which is constant due to the force applied never changing which is 2*S/t^2, I've also calculated the angular acceleration which is acceleration/radius in rad/s^2. Force P acting in the wire is m(9.81-a) I have also calculated as well the torque Which is P*radius of shaft.
 
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  • #4
If you've calculated the torque and the angular acceleration, you have all you need to find the rotational inertia: [itex]\tau = I \alpha[/itex].
 
  • #5
I thought of that but was unsure whether I could use that equation for this problem, thanks for your help :biggrin:
 

1. What is moment of inertia and why is it important?

Moment of inertia is a measure of an object's resistance to rotational motion. It is important because it helps us understand how objects behave when they are rotating, and it is essential in calculations involving rotational motion and energy.

2. How is moment of inertia calculated?

Moment of inertia is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. For more complex shapes, the moment of inertia is calculated by integrating the mass distribution over the entire object.

3. What is the difference between moment of inertia and mass?

Moment of inertia is not the same as mass. Mass is a measure of an object's resistance to linear motion, while moment of inertia is a measure of an object's resistance to rotational motion. In simpler terms, moment of inertia takes into account not only the mass of an object, but also how that mass is distributed in relation to the axis of rotation.

4. How does moment of inertia affect an object's rotational motion?

Moment of inertia affects an object's rotational motion by determining how much torque is required to change the object's rotational speed. Objects with a larger moment of inertia will require more torque to change their rotational motion, while objects with a smaller moment of inertia will require less torque.

5. How can moment of inertia be used in practical applications?

Moment of inertia is used in many practical applications, such as designing machines and structures that involve rotational motion, such as bicycles, cars, and buildings. It is also important in understanding the behavior of objects in space, such as satellites and planets.

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