Question

How can a force (e.g., a muscle force or a gravitational force) produce a translatory and a linear force simultaneously?

Answer 1

If you apply Force in a way that your force vector intercept the center of mass (CM) of an object you’ll produce a linear movement on the said object. Take a dice for example (it’s center of mass is pretty much in the center of the cube), if you put it on a table and push it all over one of it’s faces, with a notebook for example, it’ll move on a straight line.

On the other side, if you apply force in a non-colinear line related to the center of mass of an object you’ll produce a Torque. However, an object with pure rotatory motion is quite difficult to get, since any force applied on the object has to be under some specifications to produce pure torque, and not a mix of torque and force (colinear to the CM). One of these is applying force at two points, at the same distance from the CM, opposite to each other and tangentially to a hypothetical sphere around the CM. The engine of a train apply force very near the far end of it’s whells, trying to maximize efficiency, since the train will not accelerate with Force, but it will with Torque.

Mixing both you have, for example, a bowling ball. The force that initiated it’s movement is not on it’s far end, and not colinear to it’s center of mass. It has both properties, linear and rotatory motion.