rotation, friction (urgent)

Zidane

2012-06-14 10:59 pm

http://farm9.staticflickr.com/8161/7185808367_28808631cb_b.jpg

1. I wanna ask is the condition for a sphere/cylinder to roll on the ground w/o sliding
'velocity of centre of mass = angular velocity x radius of that object'?

2. for the first diagram, a cylinder is rolling down the ramp w/o sliding, and then it collides with the wall elastically. The horizontal ground has friction.
The solution to the question says the friction does no work on the cylinder when it is still rolling on the horizontal ground before hitting the wall. Why?
The direction of friction is along the ground, and the displacement of the cylinder is also along the ground, so why is work done=0?

3. for the second diagram, a wedge is placed on a smooth floor, with a cylinder rolling down the inclined plane without sliding. Again, the solution says the friction between the cylinder and the wedge is static friction and will not cause any loss in mechanical energy, why?
And what will happen if no friction exists between the cylinder and the wedge? The cylinder won't 'roll'?

thanks

回答 (1)

天同

2012-06-14 11:53 pm

✔ 最佳答案

1. Yes, the specified relation holds if a ball/cylinder rolls without slipping.

2. It is because the point of contact of the cylinder with the ground is stationary for the cylinder to roll without slipping. As such, friction does no work. This is similar to the case that when you push a box on a rough ground with a force smaller than the maximum frictional force, the box doesn't move and there is no work done by friction.

3. The reason is the same as that given in (2) above.
If the wedge surface is smooth, the cylinder just slides down the incline. It would not roll. You need frictional force to start the cylinder rolling on the wedge.

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