Question

derive an expression for the equation of motion which governs the motion of centre of mass​

Answer 1

The center-of-mass (COM) is the single point on a structure that characterizes the motion of the object if the object shrinks to a point mass.

Explanation:

• If a net force is applied to the COM the resulting motion will be translated (the object will not rotate).
• If a net force is applied to some other location on the object, the object will both translate and rotate about its COM.

1-D Linear motion

The object is struck to the left of the COM so that it translates and rotates clockwise about the COM. Notice, once again, that the COM moves in the same straight line as it did when the impact was at the COM. This again illustrates that the COM is the single point that characterizes the translational motion of the object.

2-D projectile motion

When the object is struck at a point above the COM, the object rotates clockwise about its COM, while at the same time the COM follows the original projectile path.

Answer 2

Answer:

ac-d2Rcm/dt2 is the equation of motion