Moment of Inertia for Rotational Kinematics

In summary, the conversation discusses finding the moment of inertia for a thin uniform rod that has been bent at its center to form two perpendicular segments. The equation used to find the moment of inertia is I = (integral) r^2 dm, and the individual moments of inertia for each rod are calculated as (m*L^2) / 12. However, the total moment of inertia is found to be (m*L^2) / 6, which differs from the initial assumption that it would be twice the moment of inertia of a bar of length L/2 and mass M/2.
  • #1
alco19357
18
0

Homework Statement


A thin uniform rod of mass (M) and length (L) is bent at its center so that the two segments are now perpendicular to each other.

a. Find its moment of inertia about an axis perpendicular to its plane and passing through the point where the two segments meet.


Homework Equations


I = (integral) r^2 dm



I have a picture drawn (attached) but don't know how to proceed from here.

Thank you for any help
 

Attachments

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  • #2
Won't the inertia be twice that of a bar of length L/2 and mass M/2 about its end?
 
  • #3
I would think that the moment of inertia would be:

I = (1/3)(m) [(L^2) / 4] for each rod...
= (m*L^2) / 12 for each rod

Therefore the total moment of inertia should be
I = (m*L^2) / 6 //sum of the two rodsBut it said that answer was wrong...

Thank you for the help
 

Related to Moment of Inertia for Rotational Kinematics

1. What is moment of inertia?

Moment of inertia is a physical property of an object that measures its resistance to rotational motion. It is a quantitative measure of how difficult it is to change an object's rotational velocity.

2. How is moment of inertia related to rotational kinematics?

Moment of inertia is a crucial factor in rotational kinematics, as it determines the amount of torque required to produce a given angular acceleration. In other words, it is directly related to an object's rotational motion.

3. How is moment of inertia calculated?

The moment of inertia of an object can be calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. It is also affected by the shape and distribution of mass within the object.

4. What is the unit of measurement for moment of inertia?

The unit of measurement for moment of inertia depends on the system of units being used. In the SI system, it is measured in kilograms per square meter (kg•m²). In the imperial system, it is measured in slug•ft².

5. How does moment of inertia differ from mass?

Mass is a measure of an object's resistance to linear motion, while moment of inertia is a measure of its resistance to rotational motion. In other words, they are two different physical properties that describe an object's behavior in different types of motion.

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