What type of motion occurs when a force is applied off-center to a freely movable object?

When a force is applied off-center to a freely movable object, it causes rotary motion. This is because the force creates a torque about the object's center of mass, resulting in a rotational movement around that point. This type of motion is governed by the principles of angular dynamics, where the direction and application of the force lead to a change in the object's angular velocity.

Translational motion involves movement along a straight line without rotation, which occurs when forces are applied directly through the center of mass. Linear motion, similarly, refers to movement in a straight path and does not account for any rotational effect. Oscillatory motion describes a repeated back-and-forth movement around an equilibrium position, typical of pendulums or springs, which isn't the case when considering the applied off-center force on the object.

Therefore, the nature of the motion induced by an off-center force emphasizes rotation, confirming that rotary motion is the correct classification for this scenario.