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Can the same force increase both the translational and rotational kinetic energy of a rigid body? If yes then the work done by the force equals the sum of the increase in the translational and rotational kinetic energy?
The dual role of force acting on a rigid body refers to the two ways in which a force can affect the motion of a rigid body. It can either cause the body to translate or rotate, or a combination of both.
A translational force is a force that causes a body to move in a straight line, while a rotational force causes a body to rotate around a fixed point or axis. Both types of forces can act simultaneously on a rigid body.
The direction of a force is important in determining whether it will cause a translational or rotational motion in a rigid body. If the force is applied at a distance from the center of mass, it will cause a rotational motion. If the force is applied at the center of mass, it will cause a translational motion.
The principle of superposition states that the effects of multiple forces acting on a rigid body are additive. This means that the resulting motion of the body will be a combination of the individual motions caused by each force acting alone.
The magnitude of a force determines the amount of translational or rotational motion it can cause in a rigid body. A larger force will cause a greater acceleration and a larger displacement, while a smaller force will cause a smaller acceleration and displacement.