Rotational Kinematics & Dynamics
A roller is made by joining together two cones at their vertices . It is kept on two rails and , which are placed asymmetrically (see figure), with its axis perpendicular to and its center at the center of line joining and (see figure). It is given a light push so that it starts rolling with its center moving parallel to in the direction shown. As it moves, the roller will tend to:
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Answer: (c)
- Each cone touches a rail where its radius equals that point's distance from O along the axis; larger distance means larger radius.
- As O moves forward, rail AB (slanting) gets closer to O, so the left contact radius decreases; CD stays at fixed distance.
- The left side then covers less distance per turn than the right side, so the roller turns towards the left.
- So the answer is (c) turn left.