Moment of Inertia of a rigid rotating object.

In summary, in this conversation, the question was posed about the distance and moment of inertia of a system consisting of two small masses attached to a massless rod. The distance, x, from mass M1 to the center of mass was found to be 1.58 m, and the moment of inertia about an axis perpendicular to the rod passing through the center of mass was calculated using the formula I = 1/3 ML^2. No calculus was needed to solve this problem.
  • #1
asz304
108
0

Homework Statement



Two small masses are attached to a massless rod of length 2.36 m as shown. Mass M1 is 2.53 kg and mass M2 is 5.16 kg. A) What is the distance, x, from mass M1 to the centre of mass of this system? B) What is the moment of inertia of this system about an axis that passes through the centre of mass and is perpendicular to the rod?


M1------------------(.)----------M2
{--------- x--------}. {---(L-x)-}

(.) is the axis of rotation.

The Attempt at a Solution



I found the answers for question A) using the formula of center of mass and my point of origin was M1.

X = 1.58 m
L-X = 0.78 m

How do I find the moment of inertia if the axis isn't at the middle? If I need to use integrals, can some please show me how? I didn't do integrals yet. thanks
 
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  • #2
asz304 said:
How do I find the moment of inertia if the axis isn't at the middle? If I need to use integrals, can some please show me how? I didn't do integrals yet. thanks
There's no need for any calculus. Treat the small masses as point masses. What's the moment of inertia of a point mass at some distance from an axis?
 
  • #3
Oh. thanks that made lots of sense. I used I = 1/3 ML^2 , and I got the right answer when I checked the computer.
 

1. What is the definition of "moment of inertia"?

The moment of inertia of a rigid rotating object is a measure of its resistance to changes in rotational motion. It is analogous to mass in linear motion, as it describes the object's tendency to continue rotating about an axis.

2. How is moment of inertia calculated?

Moment of inertia is calculated by multiplying the mass of each particle in the object by the square of its distance from the axis of rotation, and then summing these values for all particles. It is expressed as I = ∫r²dm, where r is the distance from the axis and dm is the differential mass element.

3. What factors affect the moment of inertia of an object?

The moment of inertia of an object is affected by its mass, shape, and distribution of mass. Objects with a larger mass or a more spread out mass distribution will have a higher moment of inertia, while objects with a smaller mass or a more compact shape will have a lower moment of inertia.

4. How does moment of inertia relate to rotational kinetic energy?

The moment of inertia is directly related to the rotational kinetic energy of an object, as it appears in the equation for rotational kinetic energy, K = ½Iω². This means that objects with a higher moment of inertia will require more energy to rotate at a given angular velocity.

5. Can the moment of inertia of an object change?

Yes, the moment of inertia of an object can change if the object's mass or distribution of mass changes. For example, if a rotating object loses or gains mass, its moment of inertia will change accordingly. Additionally, changes in the shape or position of the object can also affect its moment of inertia.

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