How Do You Calculate Angular Velocity and Moment of Inertia?

[edeffect]

Hey

Just trying to work out this question (see image). Solving for I (see other image) in an effort to find the angular velocity. Could someone have a look at this working and tell what I am doing right and wrong?

Thanks Heaps

Ed

 

[dynamicsolo]

There is not only going to be rotational kinetic energy, but translational KE as well. After all, the center of masses of both bars are falling and are also moving toward each other, as the system collapses toward the central axis of symmetry.

 

[baba89]

Hi Ed,

It looks like you are on the right track with solving for angular velocity by finding the moment of inertia first. Remember that moment of inertia is the measure of an object's resistance to changes in its rotation, and it is dependent on the object's mass and how that mass is distributed around its axis of rotation.

To find the moment of inertia, you need to first identify the axis of rotation. In the image you provided, it looks like the axis of rotation is at the center of the object. From there, you can use the formula I = mr^2, where m is the mass of the object and r is the distance from the axis of rotation to the mass element.

Next, you can use the formula for angular velocity, which is ω = v/r, where v is the linear velocity and r is the distance from the axis of rotation to the point where you want to find the angular velocity.

It's important to keep track of your units and make sure they are consistent throughout your calculations. Also, double check your math to make sure you have the correct values plugged into the equations.

I hope this helps, and good luck with your calculations! Let me know if you have any further questions.