Wooden State Maps, 1J10.11

Topic and Concept:

• 1J10. Statics of Rigid Bodies, Finding the Center of Gravity

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Location:

• Cabinet: Mechanic (ME)

• Bay: (A6)

• Shelf: #4

Abstract:

Suspend a map of the state from holes drilled at various points to find the "center of the state".

Important Setup Notes:

• N/A

Setup and Procedure:

1. Instead of a weighted rod stand as pictured, a rod clamped to the lecture bench works well too.
2. Make sure there are two smaller rods cantilevered off the vertical rod.
3. From each eyebolt, suspend the wooden state, and hang the plumb bob from the higher rod.
4. For each suspension point, trace a line along the string of the plumb bob using a dry-erase marker.
5. Draw a point on the location where all of these lines intersect. This is the center of gravity.

Cautions, Warnings, or Safety Concerns:

• N/A

Discussion:

The orientation of the state map while suspended from the rod is determined by the collective effect of gravity on each mass element of the map. For each point of mass in the board not in the center of mass, there will be a torque on the board due to gravity. The equilibrium orientation of the state map is the configuration of zero torque. The center of mass will always be located under the suspension point (on the line traced by the plumb bob). The point where all these lines intersect is the point where the sum of the position vectors for every mass element, weighted by mass, is zero. I.e. where Σ_i r_i * m_i = 0.

Videos:

• Lecture Demonstration's Youtube Channel

References:

• Center of Gravity (Center of Mass) - Wikipedia

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