Final answer:
A round object cannot undergo rolling motion on a frictionless incline because friction is required to initiate the rotational component of rolling.
Step-by-step explanation:
Can a round object released from rest at the top of a frictionless incline undergo rolling motion? The answer is no. Rolling motion entails both translational (lineal) and rotational movement. However, without friction, there would be no force to start the rotational movement.
Instead, the object would simply slide down without rolling because friction is necessary to create the torque that initiates rotation.
A round object released from rest at the top of a frictionless incline can undergo rolling motion. When the object is released, it will gain both translational and rotational kinetic energy.
As it rolls down the incline, the gravitational potential energy is converted into both forms of kinetic energy. This allows the object to maintain a constant speed while also rotating.