OK, I Agree
4.1.3 Centres of Mass
What is meant by the centre of mass of an object?
The centre of mass of an object is
the point at which the weight of the object may be considered to act For a
the centre of mass is at the centre of the object where the lines of symmetry intersect
uniform this will be at its midpoint rod For a
uniform rectangular this will be where the diagonals intersect lamina
non-uniform object the centre of mass is not necessarily at the centre of the object How can I solve problems involving uniform rods? If you are told that a rod is uniform then you can draw the weight at the midpoint of the rod If a rod lies on a support or peg then there will be a normal reaction force which acts perpendicular to the rod at that point If the rod is suspended by strings or cables then there will be tensions in the strings which keep the rod in place
If there are two supports with unknown reaction forces then choosing the pivot to be at one of the supports will help to find the force at the other support. The same method works with strings too.
How do I find the centre of mass of a non-uniform rod in equilibrium?
Step 1: Label the weight of the rod at a random point on the rod
Step 2: Call the perpendicular distance between the pivot and the weight x
Or any letter of your choice
Step 3: Form a moment equation using the fact that the rod is in equilibrium
Step 4: Solve the equation to find x
Make sure you read carefully which distance you are asked to find.