03-04-2012, 11:51 AM
Finding the center of mass of a flat irregular-shaped object
[attachment=19386]
Philllip K. Bigelow
Fig. 1
It is sometimes difficult to accurately determine the center of mass of irregularly-shaped
flat objects, such as the weirdly-formed plate illustrated above (Fig. 1). Here is one
well-known method that always yields excellent results. The method has been in use for
at least two hundred fifty years, but its discovery is probably ancient. Note: In order for
this method to work well, the object must have a uniform thickness.
Step 1) Cut a length of string that is at least as long as the longest dimension of the object
that you are measuring. Attach a weight (such as a lead fishing sinker) to one end. Tie a
small loop at the opposite end of the string.
Step 2) Place a small dot at 3 randomly-placed locations on the object, each dot located
near an edge (Fig. 2).
Fig. 2
Step 3) Using a pin or a nail, punch a hole through each dot. Insert a pin or tack through
one of the holes (Fig. 3). If the object is hard, then you will have to drill a hole in the
object. Important: The hole should be slightly larger than the diameter of the
pin or nail (in other words, the hole should be big enough so that the object rotates
freely on the mounting pin). Then, using the same pin/nail as a hanging attachment,
attach the object onto a vertically-oriented cork board or to a similar vertical wall. Make
sure that the object can swing freely, with no resistance and no binding.
Fig. 3
Step 4) Next, attach the string with its attached weight onto the pin/nail (Fig. 4). The
weight should hang straight down, with the string perfectly aligned with the "g" (gravity)
vector. The string with its attached weight is your plumb line.
Fig. 4
Step 5) Trace the line of the string onto the object with a pencil or other marker. This step
is where you must be very precise. One easy way to do this is to use as one end point the
hole from which the string is hanging. Then place a mark on the object, directly under the
string, close to its opposite end (to facilitate this, you can shine a flashlight’s beam at
exactly... really...I mean exactly 90 degrees to the surface of the object, and then place
your mark along the shadow that is being cast by the string. Do not touch the string,
itself). Lastly, use a straight edge (ruler) to help you draw a straight line between these
two points.
Step 6) Remove the pin from the object and place the pin in the second hole. Re-hang the
object and repeat the same procedure. Repeat the procedure with the third hole. When you
have finished, you will have drawn three lines on the object (Fig. 5).
Fig. 5
Step 7) The center of mass should be at the intersection of the three lines (Fig. 5, above).*
Note: It should be obvious, even to the casual observer, that only two lines are needed
to find the object's center of mass. The 3rd line is only used to check the accuracy of your
methodology (were you sloppy in step 5?). If all three lines don't meet at a single point,
then repeat the process from the beginning (using the same three holes). Make sure that
the object can rotate freely on its pin with no resistance.
* To be precise, the center of mass is under the green-colored point, inside the plate,
exactly half-way through its thickness.
Hell Creek Life © 1997-2009 Phillip Bigelow
[attachment=19386]
Philllip K. Bigelow
Fig. 1
It is sometimes difficult to accurately determine the center of mass of irregularly-shaped
flat objects, such as the weirdly-formed plate illustrated above (Fig. 1). Here is one
well-known method that always yields excellent results. The method has been in use for
at least two hundred fifty years, but its discovery is probably ancient. Note: In order for
this method to work well, the object must have a uniform thickness.
Step 1) Cut a length of string that is at least as long as the longest dimension of the object
that you are measuring. Attach a weight (such as a lead fishing sinker) to one end. Tie a
small loop at the opposite end of the string.
Step 2) Place a small dot at 3 randomly-placed locations on the object, each dot located
near an edge (Fig. 2).
Fig. 2
Step 3) Using a pin or a nail, punch a hole through each dot. Insert a pin or tack through
one of the holes (Fig. 3). If the object is hard, then you will have to drill a hole in the
object. Important: The hole should be slightly larger than the diameter of the
pin or nail (in other words, the hole should be big enough so that the object rotates
freely on the mounting pin). Then, using the same pin/nail as a hanging attachment,
attach the object onto a vertically-oriented cork board or to a similar vertical wall. Make
sure that the object can swing freely, with no resistance and no binding.
Fig. 3
Step 4) Next, attach the string with its attached weight onto the pin/nail (Fig. 4). The
weight should hang straight down, with the string perfectly aligned with the "g" (gravity)
vector. The string with its attached weight is your plumb line.
Fig. 4
Step 5) Trace the line of the string onto the object with a pencil or other marker. This step
is where you must be very precise. One easy way to do this is to use as one end point the
hole from which the string is hanging. Then place a mark on the object, directly under the
string, close to its opposite end (to facilitate this, you can shine a flashlight’s beam at
exactly... really...I mean exactly 90 degrees to the surface of the object, and then place
your mark along the shadow that is being cast by the string. Do not touch the string,
itself). Lastly, use a straight edge (ruler) to help you draw a straight line between these
two points.
Step 6) Remove the pin from the object and place the pin in the second hole. Re-hang the
object and repeat the same procedure. Repeat the procedure with the third hole. When you
have finished, you will have drawn three lines on the object (Fig. 5).
Fig. 5
Step 7) The center of mass should be at the intersection of the three lines (Fig. 5, above).*
Note: It should be obvious, even to the casual observer, that only two lines are needed
to find the object's center of mass. The 3rd line is only used to check the accuracy of your
methodology (were you sloppy in step 5?). If all three lines don't meet at a single point,
then repeat the process from the beginning (using the same three holes). Make sure that
the object can rotate freely on its pin with no resistance.
* To be precise, the center of mass is under the green-colored point, inside the plate,
exactly half-way through its thickness.
Hell Creek Life © 1997-2009 Phillip Bigelow