Cylinder rolling on fixed cylinder

In summary, the conversation is about finding the equations for motion, specifically in relation to a cylinder losing contact. The person asking for help needs the information for a test the following day. The other person suggests using a differential equation and asks about the values of a and b, which were not mentioned in the problem statement. They also advise the first person to double check the kinematics aspect to avoid getting off track.
  • #1
Snehit
3
0
Check Attached file for questionI am not able to get the equations for motion. Except that when cylinder loses contact, the normal force is zero.Please answer this fast. Need it for a test tomorrow. Thanks a lot!
 

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  • #2
Ok, I tried the question for some time and came up with this differential equation,

\ddot{\theta} + \frac{2g}{3(a+b)} \sin(\theta) = 0
 
  • #3
What are a and b; they do not appear in the problem statement.

Did you get the kinematics correct? This is where most people get off track on a problem of this sort, so look very closely at that aspect.
 

What is "cylinder rolling on fixed cylinder"?

"Cylinder rolling on fixed cylinder" refers to a physical phenomenon where a cylindrical object, such as a wheel or a ball, rolls along the surface of another cylinder without slipping.

What is the difference between rolling and sliding?

Rolling is a type of motion in which an object moves along a surface without slipping, whereas sliding is a type of motion in which an object moves along a surface while experiencing friction. In rolling, the point of contact between the object and the surface remains stationary, while in sliding, the point of contact moves along the surface.

What factors affect the speed of a cylinder rolling on a fixed cylinder?

The speed of a cylinder rolling on a fixed cylinder is affected by the radius of the cylinders, the coefficient of friction between the cylinders, and the mass and rotational inertia of the rolling cylinder. Other factors such as the surface texture and the angle of the incline may also affect the speed.

How does the shape of the rolling cylinder affect its motion on the fixed cylinder?

The shape of the rolling cylinder affects its motion on the fixed cylinder in various ways. For example, a cylinder with a larger diameter will roll faster than a cylinder with a smaller diameter. Additionally, a cylinder with a larger mass or rotational inertia will require more force to accelerate and maintain its motion on the fixed cylinder.

What are some real-world applications of cylinder rolling on fixed cylinder?

Cylinder rolling on fixed cylinder is a commonly observed phenomenon in everyday life, such as the rolling of a wheel on a road or the movement of a ball on a playground. This principle is also utilized in various mechanical systems, such as gears and pulleys, and in the design of vehicles and machinery.

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