How can the total horizontal force on a rolling ball be shown to be zero?

In summary, when a ball is rolling without slipping on a horizontal plane, the total horizontal force on the ball must be zero. This can be shown by considering the ball as a rigid body and combining equations describing rotation with rolling constraints. The ball's translational and rotational velocities will be constant, indicating that F=ma. However, this statement is not entirely correct as you can accelerate a ball on a horizontal plane by applying a net force. The only constraint is that the ball is not slipping, which allows for the normal force to be equal to mg.
  • #1
Logarythmic
281
0
How can I show that when a ball is rolling without slipping on a horizontal plane, the total horizontal force on the ball must be zero?

I guess I should consider the ball as a rigid body and combine the equations describing the rotation with the rolling constraints, but how? Can someone give me a starter here?
 
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  • #2
The statement is not correct. I think you meant to say that it is rolling at a constant velocity without slipping. If it's translational and rotational velocities are constant, then what can you say about F=ma?

But you can definitely accelerate a ball on a horizontal plane by applying a net force...
 
  • #3
The problem says nothing about constant velocity, just that the ball is constrained to move on a horizontal plane. Otherwise, a = 0 and F = 0.
 
  • #4
When the ball is not slipping, you can say something about the normal force.
 
  • #5
Yeah, equal to mg?
 
  • #6
edit: nevermind.
 
Last edited:

1. What is a rolling constraints problem?

A rolling constraints problem is a type of optimization problem that involves finding the optimal path or solution for a moving object subject to certain constraints. This can include constraints such as maximum velocity, minimum turning radius, or avoiding obstacles.

2. What are some real-world applications of rolling constraints problems?

Rolling constraints problems have many applications in industries such as robotics, transportation, and manufacturing. Some examples include route planning for self-driving cars, optimizing delivery routes for logistics companies, and designing efficient assembly lines for factories.

3. How are rolling constraints problems typically solved?

There are various approaches to solving rolling constraints problems, but the most common method is using mathematical optimization techniques. This involves formulating the problem as a mathematical model and using algorithms to find the optimal solution.

4. What are some challenges that may arise when solving rolling constraints problems?

One of the main challenges with rolling constraints problems is the complexity of the optimization process. As the number of constraints and variables increases, the problem becomes more difficult to solve. Additionally, real-world factors such as uncertainty and dynamic environments can also make these problems more challenging.

5. How can rolling constraints problems be applied to improve efficiency and performance?

By solving rolling constraints problems, we can find the most efficient and optimal solutions for various real-world scenarios. This can lead to improved performance and cost savings in industries such as transportation and logistics. Additionally, solving these problems can also help in the development of advanced technologies such as autonomous vehicles and smart manufacturing systems.

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