Clarification regarding rolling cylinder with CG slightly above

In summary, the conversation is about a rolling cylinder on an inclined plane and the work done by rolling friction and normal reaction. The person asks for clarification on the work done by rolling friction and normal reaction, and provides their own calculations for both. They also mention that they are aware of the work done by normal reaction being zero for a cylinder with center O.
  • #1
seshikanth
20
0
Hi

Can anyone please clarify the following?

Let there by a rolling cylinder on an inclined plane. Let the solid cylinder(with Center O) on the inclined plane has Center of gravity at a distance 'c' slightly above O. If the cylinder is displaced slightly through an angle θ then

[Let N = normal reaction; F= Rolling friction]

1. What is the work done by rolling friction F
I think, W1 = F. c Sinθ. ---- Can you tell am i correct here?

2. What is the work done by Normal Reaction?
I think it is W2 = R. (c - c Cosθ) ; --- Can you tell me if i am correct here? I know that the work done by normal reaction for a cylinder with center O as zero !



Thanks,
 
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  • #2
Can anyone have a look at this?

Thanks,
 
  • #3
gentle reminder
 

Related to Clarification regarding rolling cylinder with CG slightly above

1. How does the location of the center of gravity affect the rolling of a cylinder?

The location of the center of gravity (CG) plays a crucial role in the rolling of a cylinder. If the CG is located exactly at the center of the cylinder, it will roll smoothly and maintain a straight path. However, if the CG is slightly above the center, it will cause the cylinder to wobble and potentially deviate from its intended path.

2. Can a cylinder with the CG slightly above still roll without wobbling?

Yes, it is possible for a cylinder with the CG slightly above to roll without wobbling. This is dependent on factors such as the surface it is rolling on, the speed at which it is rolling, and the overall stability of the cylinder. However, it is more likely for the cylinder to wobble with the CG above the center compared to when the CG is at the exact center.

3. How does the diameter of the cylinder affect its stability when the CG is slightly above?

The diameter of the cylinder plays a significant role in its stability when the CG is slightly above the center. A larger diameter cylinder will have a lower center of gravity, making it less likely to wobble compared to a smaller diameter cylinder with the same CG location. This is because a larger diameter cylinder has a wider base, providing more stability.

4. What are the potential consequences of a cylinder rolling with the CG slightly above?

The main consequence of a cylinder rolling with the CG slightly above is instability and potential deviation from its intended path. This can lead to problems in applications where precise movement is required, such as in robotics or machinery. It can also increase the risk of the cylinder tipping over, especially if the surface it is rolling on is not completely flat.

5. How can the CG of a cylinder be adjusted to prevent instability when rolling?

The CG of a cylinder can be adjusted by changing the distribution of weight within the cylinder. This can be achieved by adding or removing weight from different parts of the cylinder. Alternatively, the cylinder can be designed with a wider base or a larger diameter to lower the CG. Additionally, the surface on which the cylinder is rolling can be modified to provide more stability, such as using a track or adding support structures.

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