Question

Does the center of mass accelerate?

Answer 1

Hint: The center of mass is a point in a system where the weighted distributed mass comes out to be zero. For simplifying calculations, the whole mass is said to be concentrated at the center of mass and it undergoes motion as the whole system. For symmetric bodies, it lies on the centroid.

Complete answer:
The center of mass is a point where the whole mass of a body is assumed to be concentrated. The centre of mass can also be defined as the average position of all components of the system or body. For symmetric bodies, the centre of mass lies at the centroid. The distributed mass of the system is zero at the centre of mass. The formula used for calculating the centre of mass is-
$R=\dfrac{\sum\limits_{i=1}^{n}{{{m}_{i}}{{r}_{i}}}}{\sum\limits_{i=1}^{n}{{{m}_{i}}}}$
Here, $R$ is the position of the centre of mass
$\sum\limits_{i=1}^{n}{{{m}_{i}}{{r}_{i}}}$ is the sum of product of mass and position of particles of a system
$\sum\limits_{i=1}^{n}{{{m}_{i}}}$ is the sum of masses of all components of a system
When an external force is applied on the centre of mass, it moves with acceleration equal to the acceleration of the whole system. When a system moves with certain acceleration, the whole mass of the system is assumed to be concentrated at the centre of mass and the center of mass is said to move with that acceleration. This is done in order to make the calculations easier.
Therefore, the center of mass accelerates with the same acceleration as the system as a whole.

Note:
The whole mass of the system is assumed to be concentrated on the centre of mass so as to assume the system as a point object. Whether the center of mass undergoes angular acceleration or not depends on the position of axis of rotation. If the axis of rotation passes through the center of mass, it does not undergo angular acceleration.