How do I find the Moment of Inertia?

In summary, the experiment involves a physical pendulum with a rod and two large rubber stoppers being swung from a point 1 mm from the end point. The moment of inertia of the pendulum about the point of suspension can be calculated using the parallel axis theorem and the moment of inertia of point masses. The data needed for the calculation includes the mass of the rod, the mass of the stoppers and bolt, the length of the rod, the distances between the center of mass and the point of suspension for both the rod and stoppers, the maximum angular displacement, and the experimental period of oscillation. The parallel axis theorem can be used to find the moment of inertia for the rod about the point of suspension, and the total moment
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Homework Statement



In this experiment a physical pendulum consisting of a rod and two large rubber stoppers (on top of each other) is swung from a point 1 mm from the end point. Calculate the moment of inertia of the pendulum about the point of suspension?

Data:
m=mass of rod=97.1 g
M=mass of the stoppers and the bolt=200 g
L=1 meter=length of rod
d=distance between the center of mass (CM) of the rod and the point of suspension=499 mm
D=distance between the center of mass of the stoppers and the Point of suspension=879 mm
R=distance between the Center of Mass of the rod-stopper system and the point of suspension=689 mm
theta (max)=the max angular displacement of the system from equilibrium (i.e. the max angular amplitude). Remember, theta (max) should be less than about pi/12 radian for the motion to be simple harmonic)=90 degrees
T(sub e)=the experimental period of oscillation of the pendulum. (measure and record at least three sets of 10 complete oscillations)=17.39 seconds/10 oscillations.
r=the distance from the center of the ruler to the point of rotation (.499 m)





Homework Equations


Note: I was sick when my teacher taught this so I learned the following from a friend.
use parallel axis theorem+MOI of point masses


(I)totalrod = (I)ruler + (I)mass

(I)mass= MR^2 where R = the distance from the center of the point mass to the rotation

and M is the mass for the point mass (200 g)

(I)ruler is the parralel axis theorem which is like

(I)ruler= (I)centerofmass + Md^2

where (I)center of mass is equal to 1/3Mr^2 where r is the distance from the center of the ruler to the point of rotation (.5 meters) + Md^2...

The Attempt at a Solution


I was sick...I don't know Sorry!
Help..eh :)
Thanks so much! This is due tomorrow so Urgency is somewhat required LOL...I wish I was smart
 
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  • #2
Well you know that Ipoint mass=mr2, so you can find the I for the masses about the point of suspension (POS).

For a rod, about its center, the moment of inertia is 1/12ML2.

Now the parallel axis theorem states that

IPOS=IC+mRPOS2

You should be able to get the I for the rod about the POS now.

Now that both of the 'I's are about the same axis, the total I about that axis, is just the sum of the individual 'I' values.
 

1. How do I calculate the moment of inertia for a point mass?

The moment of inertia for a point mass can be calculated using the formula I = mr^2, where m is the mass of the point and r is the distance from the point to the axis of rotation.

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

The moment of inertia is a measure of an object's resistance to rotational motion, while mass moment of inertia is a measure of an object's resistance to both translational and rotational motion. Mass moment of inertia takes into account the distribution of mass within an object.

3. How do I find the moment of inertia for a continuous object with varying density?

To find the moment of inertia for a continuous object with varying density, the object is divided into small elements and the moment of inertia for each element is calculated using the formula I = m*r^2. These individual moments of inertia are then summed to find the overall moment of inertia for the object.

4. Can the moment of inertia be negative?

No, the moment of inertia cannot be negative as it is a measure of an object's resistance to rotational motion and must always be a positive value.

5. What are the units of moment of inertia?

The units of moment of inertia depend on the units of mass and distance used in the calculation. In the SI system, the units are kg*m^2, while in the US customary system, the units are lb*ft^2.

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