Ball rolling on a larger ball on a surface

[theQM123]

I've just been wondering about this kind of problem. Let m be the mass of the smaller ball, and M be the mass of the larger ball. Assuming the ball does not slip and that the surfaces are frictionless, what is the time that it takes for the smaller ball to reach the bottom/floor if the the radii for the small and large ball are 2m and 10m respectively?

What does it become when there is friction with a coeffecient of 0.2?

 

[mfb]

If there is no static friction the balls will slip.

What did you find out so far?

 

[theQM123]

The thing is, I don't quite know where to start.

 

[PeroK]

The thing is, I don't quite know where to start.

If there is no friction, then neither ball will roll and both will slide. If there is friction, then they may both roll, although the smaller ball will eventually slip before it falls off.

Also, the time for this motion is indeterminate unless you specify an initial velocity and/or angle for the small ball.

There is actually another post at the moment, where someone has posted a similar problem:

https://www.physicsforums.com/threa...f-a-rough-spherical-dome.808105/#post-5072564

There is a simpler problem, where the large ball is fixed and there is no friction. In that case, you have to work out how far the small ball slides before it falls off. Even that, however, is not that easy a problem. It too, was posted on here a while back.

And, for this problem too, the time is indeterminate.

 

[mfb]

The thing is, I don't quite know where to start.

With relevant equations, for example. With conserved quantities. With things you know, with things you want to know, ...
With an easier problem, as PeroK sugggested.

There are tons of possible ways to start even if you have no idea how to approach the problem as a whole.