Ball rolling on a larger ball on a surface

In summary, it might be helpful to first try to find the equations that govern the motion, and then work out what variables need to be specified in order to find the time.
  • #1
theQM123
6
0
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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?
 
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  • #2
If there is no static friction the balls will slip.

What did you find out so far?
 
  • #3
The thing is, I don't quite know where to start.
 
  • #4
theQM123 said:
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.
 
  • #5
theQM123 said:
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.
 

1. How does the size of the larger ball affect the speed of the smaller ball?

The size of the larger ball does not directly affect the speed of the smaller ball. However, it does affect the surface area in contact with the surface, which can impact friction and rolling resistance. In general, a larger ball will have more surface area in contact with the surface, resulting in more friction and slower speed for the smaller ball.

2. What factors influence the rolling motion of the smaller ball on the larger ball?

The rolling motion of the smaller ball on the larger ball is influenced by several factors, including the size and weight of the balls, the surface materials, and the force applied to the smaller ball. Additionally, factors such as the shape and texture of the balls can also play a role in the rolling motion.

3. Can the smaller ball roll in both directions on the larger ball?

Yes, the smaller ball can roll in both directions on the larger ball. This is because the direction of the rolling motion is determined by the force applied to the smaller ball, rather than the size or shape of the larger ball.

4. How does the surface material affect the motion of the smaller ball on the larger ball?

The surface material can greatly impact the motion of the smaller ball on the larger ball. A smooth and flat surface will allow for easier and faster rolling, while a rough or uneven surface can create more friction and slow down the rolling motion. Additionally, the type of material can also affect the amount of bouncing or bouncing back of the smaller ball on the larger ball.

5. What is the relationship between the mass of the smaller ball and its speed on the larger ball?

The mass of the smaller ball does not directly affect its speed on the larger ball. However, a heavier ball may require more force to start rolling and may also experience more resistance. This can result in a slower speed compared to a lighter ball. However, other factors such as the surface materials and force applied can also influence the speed of the smaller ball on the larger ball.

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