Will the 2 dimensional sphere rotate?

In summary: I see what you mean. In summary, the 200kg sphere in contact with two walls, one with no coefficient of friction and the other with μ=0.25, will not rotate when a force F=400N is applied because the torque of F is greater than the torque of T, and the sum of vertical forces does not exceed 0.
  • #1
PhysicS FAN
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4

Homework Statement


A 200kg sphere is in touch with two walls. The horizontal wall has no coefficent of friction and the vertical has μ=0.25. If we apply a force F=400N will the sphere rotate?

Homework Equations

The Attempt at a Solution

[/B]
What I can't understand is, if there is balance in the y and x-axis beacuse if so the problem is easily solved. I proved it theoritically but I can not find a mathematical solution. Please help me.
 

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  • #2
I am missing a force (*) in your drawing. Can you post your theoretical proof ?

[edit] (*) unless the B has a specific meaning
 
  • #3
BvU said:
I am missing a force (*) in your drawing. Can you post your theoretical proof ?

[edit] (*) unless the B has a specific meaning
Sorry my fault, B is representing a point not a force. The theoritical proof is that in order for the sphere to rotate, the torque of F should be bigger than the torque of T. Its clear that both T and F are in the same distance from the center K which means we can now compare F and T as forces. The biggest value of T is always less than F since T=μ*N=0.25*N and N the reaction of the verticall wall is not big enough to cause balance.
 
  • #4
PhysicS FAN said:
torque of T
Good you mention it. I can now even distinguish a T in the picture.

I agree with your reasoning and wonder why you have difficulty with the force balances: if you write then in full (i.e. ##\ \vec a = \displaystyle \sum \vec F\ \ ##) there should be no problem. Clearly there is no acceleration to the right, so the reaction force from the wall to the left is equal to F. That gives you the magnitude of T as you used it.

[edit] the next line is based on a wrong assumption:
Note that even when ##\mu = 1 \;##, nothing happens since the sum of vertical forces won't exceed 0.

[edit] the wrong assumption being: nothing happens with ##\mu = 0.25 \;##
 
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  • #5
BvU said:
Good you mention it. I can now even distinguish a T in the picture.

I agree with your reasoning and wonder why you have difficulty with the force balances: if you write then in full (i.e. ##\ \vec a = \displaystyle \sum \vec F\ \ ##) there should be no problem. Clearly there is no acceleration to the right, so the reaction force from the wall to the left is equal to F. That gives you the magnitude of T as you used it.

Note that even when ##\mu = 1 \;##, nothing happens since the sum of vertical forces won't exceed 0.
Yeah
 

1. Will the 2 dimensional sphere rotate on its own?

No, a 2 dimensional sphere cannot rotate on its own as it only has two dimensions and lacks the necessary components to rotate, such as an axis or angular momentum.

2. Can a 2 dimensional sphere be rotated by an external force?

Yes, a 2 dimensional sphere can be rotated by an external force, such as a person physically moving it or a machine applying torque to it. However, the concept of rotation may be different in two dimensions compared to three dimensions.

3. What would be the axis of rotation for a 2 dimensional sphere?

A 2 dimensional sphere does not have an axis of rotation as it only exists in two dimensions. In three dimensions, the axis of rotation is the imaginary line around which an object rotates, but this concept does not apply in two dimensions.

4. Can a 2 dimensional sphere rotate in different directions?

No, a 2 dimensional sphere can only rotate in one direction as it only has two dimensions. In three dimensions, an object can rotate in multiple directions around different axes, but in two dimensions, this is not possible.

5. What would happen if a 2 dimensional sphere was rotated in a higher dimension?

It is impossible for a 2 dimensional sphere to exist or rotate in a higher dimension. The concept of dimensions is a fundamental aspect of our universe and a 2 dimensional object cannot exist or behave in a higher dimension.

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