Torque the vector cross product, p is the particle's linear momentum, and r is the displacement vector from the origin (the origin is assumed to be a fixed location anywhere in space). The time-derivative of this is: This result can easily be proven by splitting the vectors into components and applying the product rule. Now using the definition of force formula_17 (whether or not mass is constant) and the definition of velocity formula_18 The cross product of momentum formula_20 with its associated velocity formula_21 is zero because velocity and momentum are parallel, so the second term vanishes. By definition, torque τ
Locating the center of mass Locating the center of mass There are several methods for locating the center of mass of a body. This method is useful when one wishes to find the centroid of a complex planar shape with unknown dimensions. It relies on finding the center of mass of a thin body of homogeneous density having the same shape as the complex planar shape. This is a method of determining the center of mass of an L-shaped object. This method is useful when one wishes to find the location of the centroid or center of mass of an object that is easily divided