Question

A force acting on a rigid body always causes both translation and rotation of that body.

true or false

Answer 1

If a single force is applied to a rigid body under the influence of no other forces, either:

1. The line of action of the force passes through the center of mass, causing a pure translation and no rotation
2. The line of action of force does not pass through the center of mass, in which case you end up with a pure rotation about an axis which does not pass through the center of mass. In other words the instantaneous axis of zero velocity induced by a single force can never be the center of mass.

If you apply an eccentric force, the center of mass of the body will undergo a linear acceleration, and the body itself will undergo an angular acceleration. In a fixed reference frame, this can be viewed as a pure rotation about a certain point, but this point will never be the center of mass of the body.