Calculate Moment of Inertia: Thin Rod, Length 3.14m, Mass 2.11kg

In summary, the moment of inertia of a uniform thin rod with a length of 3.14 m and mass of 2.11 kg can be found using the equation 1/12 * M *L^2 if the axis is in the center of the rod. However, if the axis is in a different position, the Parallel Axis or Steiner's Theorem can be used. The Parallel Axis Theorem states that the moment of inertia is equal to the moment of inertia about the center of mass plus the product of the mass and the squared distance from the center of mass to the new axis. This can be represented by the equation I = I(cm) +Mh^2. The term I(cm) is equal to
  • #1
ViewtifulBeau
50
0
A uniform thin rod has a length 3.14 m and mass 2.11 kg. Find the moment of inertia in kg-m2 about an axis that is perpendicular to the rod and passes through the rod at a distance of 0.67 m from the end of the rod.

I know that if the axis was in the center of the rod the equation would be 1/12 * M *L^2 . M =mass L = length.

I don't know what to do with the axis being in a different place. is it the same eqation(doubt it) or the left half minus the right half or what?
 
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  • #2
Use the Parallel axis or Steiner's Theorem.
 
  • #3
Have you heard of the Parallel Axis Theorem?
 
  • #4
Did you learn about the parallel axis theorem?
 
  • #5
hahahahaha
 
  • #6
ECHO, Echo, echo! ;)
 
  • #7
well thanks for the quick relpies, ummm yeah here in my book it is I = I(cm) +Mh^2

is I(cm) = 1/12 * M *L^2?
M is total mass
and h would be... distance from the center of mass?
 
  • #8
This is true.
 

1. What is the formula for calculating moment of inertia for a thin rod?

The formula for calculating moment of inertia for a thin rod is I = (1/12) * m * L^2, where I is the moment of inertia, m is the mass of the rod, and L is the length of the rod.

2. How do you find the mass of an object for calculating moment of inertia?

The mass of an object can be found by using a scale or balance. The mass should be measured in kilograms (kg) for standard units.

3. How do you convert meters to centimeters for calculating moment of inertia?

To convert meters to centimeters, you can multiply the length in meters by 100. In this case, the length of the rod would be 314 centimeters (3.14m * 100 = 314cm).

4. Can you calculate moment of inertia for a rod with non-uniform mass distribution?

Yes, the formula for calculating moment of inertia for a non-uniform rod is I = ∫r^2 dm, where r is the distance from the axis of rotation to the infinitesimal mass element dm. This integral can be evaluated using calculus.

5. What is the unit for moment of inertia?

The unit for moment of inertia depends on the units used for mass and length. In this case, the unit for moment of inertia would be kg*m^2.

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