## srijit 3 years ago if the velocity of the point of contact in ideal and pure rolling motion at any instant is 0 then how is the body moving and the point of contact doesn't remain stationary?

1. Vincent-Lyon.Fr

Because it's a different point of contact at each different instant. For a circular wheel rolling on a straight base, each point of contact on the wheel will move in a cycloid. Only at the cusp on the cycloid is the instantaneous velocity zero.

2. srijit

yeah but if at a particular instant if the velocity at the point of contact is 0 and neither velocity of centre of mass is changing nor the 'wR' angular velocity changes..then how is another point on the circumference coming down to replace the previous point of contact?

3. Vincent-Lyon.Fr

Because the process is continuous.

4. srijit

|dw:1357211630512:dw| a guy rolls a cylindrical drum by pushing the board across the top. so in this case what length of board rolls over the top of drum? how far does the guy walk?? (no sliding of the board with the drum and no sliding with ground) particularly i am not getting the second question.

5. Vincent-Lyon.Fr

|dw:1357213610576:dw| Point of contact with ground I has velocity 0 and is the instantaneous centre of rotation. Centre of drum C moves at velocity v = ωR Top point A, which is twice as far from I as C will have velocity 2v = ω(2R) So plank, not sliding on top of drum will move at velocity 2v relative to the ground. When centre of drum C moves a distance L/2, then plank will move L relative to the ground and will move L – L/2 = L/2 relative to the axis of the drum. So answer is : - L/2 rolls over the cylinder - the guy walks L

@ srijit......the velocity at point of contact is zero with respect to the contact point....not with respect to you or any other point......u have to change ur refrence point i.e. contact point

7. Vincent-Lyon.Fr

To be more specific, the velocity at bottom contact point is zero with respect to the ground.

8. srijit

@adi171 thanx.. @Vincent-Lyon.Fr -yeah i perfectly got what you said but the problem is resnick halliday has got the answer to be 3L/2

9. Vincent-Lyon.Fr

I don't know who Resnick Halliday is, but use a ruler and toilet paper inner cardboard roll as drum, and experiment. You will see that if drum is move by x, then plank rolls by x and moves wrt ground by 2x.

10. Vincent-Lyon.Fr

*is moved

11. srijit

sorry that is the name of an author of a physics book..ok thanx i got it! :)

12. Vincent-Lyon.Fr

Either there's a mistake in the answer of in the question itself.

13. srijit

yeah exactly..!

14. srijit