Moment of Inertia for a uniform wire

In summary, the conversation discusses finding the moment of inertia of a flat object consisting of a circle and square welded together. The mass of the circle is M and the mass of the square is m with a side length of d. Using the perpendicular axis theorem, the moment of inertia of the square about Axis B is 1/4md^2. The moment of inertia of the circle about a perpendicular axis at its center is M*r^2. The perpendicular axis theorem is then used again to find the moment of inertia of the square about the same perpendicular axis, and then both moments of inertia are added to get the total moment of inertia about Axis A. Finally, using the theorem again, the moment of inertia about Axis A is found
  • #1
SalsaOnMyTaco
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Homework Statement


A flat object shown here consists of a circle and square made of heavy, uniform wire and welded together at the corners of the square. The mass of the circle is M. The mass of the square is m and its side has a length d. To find the objects moment of inertia about Axis A:
a)Find Moment of inertia of the square about Axis B in its plane.
- I=1/4 md2

b)Find Moment of inertia of the circle about the axis perpendicular to its plane at its center C.
- I came up wit I=Mr2 (Not sure if its right?)

c)Use the perpendicular axis theorem to find the moment of inertia of the square about this same perpendicular axis.

d)Add to get the total moment of inertia about this Axis.

e)Use the perpendicular axis theorem again to get the moment of inertia about Axis A.

Homework Equations


I=ICM + Mh2

IZ=IX + IY (not sure how this theorem works)
 

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  • #2
Actually I think I figured out B.
Iz=Ix+Iy
By symmetry Ix=Iy

So
2Ix=Iz Iz=Md^2/4
Ix=1/2Iz

Iz=md^2/8

Is this correct?
 
Last edited:

What is Moment of Inertia for a uniform wire?

Moment of Inertia for a uniform wire is a physical property that measures an object's resistance to changes in its rotational motion. It is denoted by the symbol I and is calculated based on the object's mass distribution and rotation axis.

How is Moment of Inertia for a uniform wire calculated?

Moment of Inertia for a uniform wire can be calculated using the formula I = (1/12) * m * l^2, where m is the mass of the wire and l is the length of the wire. This formula assumes that the wire has a uniform mass distribution and is rotating about its center of mass.

Why is Moment of Inertia important in physics?

Moment of Inertia is important in physics because it helps us understand and predict an object's rotational behavior. It is used in various equations to calculate the torque, angular acceleration, and angular momentum of a rotating object.

How does Moment of Inertia affect an object's rotational motion?

The higher the Moment of Inertia of an object, the harder it is to change its rotational motion. This means that objects with a higher Moment of Inertia will require more torque to rotate and will have a slower angular acceleration. On the other hand, objects with a lower Moment of Inertia will have a faster angular acceleration and will be easier to rotate.

Can Moment of Inertia be affected by external factors?

Yes, Moment of Inertia can be affected by external factors such as the object's mass distribution, shape, and rotation axis. For example, a longer wire will have a higher Moment of Inertia compared to a shorter wire with the same mass. Additionally, the Moment of Inertia of an object can also change if its mass distribution is altered, such as by adding or removing mass at different points along the object.

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