Why is the CM of a 1.00m length of pipe at its midpoint, whereas this is not true for your arm or leg?
the cm is in the center only for a UNIFORM pipe. If it has one fat end, the cm is not in the center.
Ok thanks, but why isn't this true for an arm or leg?
The reason the center of mass (CM) of a 1.00m length of pipe is at its midpoint is because the pipe is symmetrical and has uniform mass distribution. Symmetry means that the mass is distributed equally on both sides of the midpoint.
To understand why this is not the case for your arm or leg, we need to consider their anatomical structure. Unlike a pipe, our limbs are not symmetrical and have non-uniform mass distribution. For example, our arms have a heavier mass at the shoulder end compared to the hand, and our legs have more mass near the hip than at the foot.
To determine the position of the CM of any object, we need to consider the distribution of mass within that object. The CM is the point where the object can be balanced, meaning that all the mass on one side is counterbalanced by mass on the other side. In the case of our arms and legs, the CM is not located at the midpoint because the mass is not evenly distributed.
To find the CM of more complex objects or body parts, we can use principles of physics and calculus. Calculating the CM requires considering the mass distribution and the position of each small element of the object. Through integration, we can find the weighted average of all these positions to determine the CM location.
In summary, the CM of a 1.00m length pipe is at its midpoint due to its symmetry and uniform mass distribution. However, the CM of our limbs, such as arms and legs, is not at the midpoint because they are asymmetrical and have non-uniform mass distribution.