Rigid body possible to reconstruct the position of all the other particles, provided that their time-invariant position relative to the three selected particles is known. However, typically a different, mathematically more convenient, but equivalent approach is used. The position of the whole body is represented by: Thus, the position of a rigid body has two components: linear and angular, respectively. The same is true for other kinematic and kinetic quantities describing the motion of a rigid body, such as linear and angular velocity, acceleration, momentum, impulse, and kinetic energy. The linear position can be represented by a vector with its tail at
Effective mass (spring–mass system) uniform linear density is 1/3 of the mass of the spring and is independent of the direction of the spring-mass system (i.e., horizontal, vertical, and oblique systems all have the same effective mass). This is because external acceleration does not affect the period of motion around the equilibrium point. We can find the effective mass of the spring by finding its kinetic energy. This requires adding all the mass elements' kinetic energy, and requires the following integral, where formula_8 is the velocity of mass element : Since the spring is uniform, formula_10, where formula_11 is the length of the spring.