Question

The motion of a cylinder on an inclined plane is:

• A. Rotational but not translational
• B. Translational but not rotational
• C. Translational but not rolling
• D. Rotational, translational and rolling motion
• E. Rotational and rolling but not translational motion

Hint:

For a rolling object, the motion is a combination of translational motion of the center of mass and rotational motion about the center. The condition \( v = r \omega \) applies when rolling without slipping.

Answer 1

The Correct Option is D

When a cylinder rolls down an inclined plane, it exhibits three types of motion:
1. Translational motion: The center of mass of the cylinder moves down the inclined plane.
2. Rotational motion: The cylinder rotates about its own axis as it moves.
3. Rolling motion: The point of contact between the cylinder and the inclined plane does not slip, which means that rolling without slipping occurs.
In rolling motion, both translational and rotational motions are coupled, and the condition for rolling without slipping is: \[ v = r \omega \] where \( v \) is the linear velocity of the center of mass, \( r \) is the radius of the cylinder, and \( \omega \) is the angular velocity.
Thus, the motion of a cylinder on an inclined plane involves rotational, translational, and rolling motions.
Thus, the correct answer is option (D), rotational, translational, and rolling motion.