If there already is horizontal motion, but no sliding, then there must already be rotation as well. So it will rotate onto the next edge.rahaverhma said:How does a polygon shaped body's toppling shifts from one edge to next adjacent edge when the object is already in motion without any sliding and no external force is applied ?
I didn't quite understand. Can you please elaborate it ?A.T. said:If there already is horizontal motion, but no sliding, then there must already be rotation as well. So it will rotate onto the next edge.
Which part?rahaverhma said:I didn't quite understand.
rahaverhma said:How does a polygon shaped body's toppling shifts from one edge to next adjacent edge when the object is already in motion without any sliding and no external force is applied ? Explain it with the case of hexagon or octagon both ways, with and without including CoM.
Drakkith said:Is this a homework question?
@rahaverhma -- All schoolwork-type questions like this go in the schoolwork forums, and you must show your best efforts on the question before we can offer tutorial help. Please re-post this in the schoolwork forums and show some diagrams and your work. This rule applies to all schoolwork-type questions, including those for self-study. Thank you.rahaverhma said:No. Explain it just conceptually without any mathematics. And one thing more please explain it both ways, with and without including CoM.
The basic principle involves the center of mass and the torque generated by gravitational forces. When the center of mass is not aligned vertically above the base of support, gravity creates a torque that causes the polygon to rotate about its edge, leading to toppling.
The shape of the polygon determines the distribution of its mass and the location of its center of mass. Polygons with a higher center of mass or a narrower base are more likely to topple, as the torque generated by gravity will be larger and more effective in causing rotation.
The polygon doesn't slide because the frictional force between the polygon and the surface is sufficient to prevent any horizontal movement. The toppling motion is primarily rotational, and the frictional force counters any potential sliding, ensuring that the motion is constrained to rotation about the edge.
Yes, a polygon can topple without any initial push or external force if it is initially positioned such that its center of mass is not vertically aligned with its base of support. In such a case, the gravitational torque will be enough to initiate the toppling motion.
The base of support is crucial in determining the stability of the polygon. A wider base of support provides greater stability, making it less likely for the center of mass to fall outside the base. Conversely, a narrower base of support makes the polygon more prone to toppling, as it takes less displacement for the center of mass to move outside the base.