Cylinder rolling on fixed cylinder

In summary, the conversation discusses a homework problem involving two cylinders, C1 and C2, where C2 is fixed and C1 starts rolling without slipping on top of it. The task is to determine the angular velocity of C1 when it loses contact with C2. The request for help is advised to be reposted in the homework section with some attempt at finding the solution, such as drawing a diagram or using Lagrangian mechanics. A hint is also given that if the trajectory is a circle, a centripetal force is needed and when it is not present, contact is lost.
  • #1
Snehit
3
0
HOMEWORK POSTED IN WRONG FORUM. WE AWAIT SOME EFFORT ON THE PART OF OP BEFORE CONTINUING.

A cylinder C1 of mass M1 and radius R1 is placed on top of another cylinder C2 of mass M2 and radius R2. C2 is kept rigidly fixed (so that it can neither translate nor rotate). C1 starts rolling without slipping on the surface of C2 (assume that the initial velocity of C1 is zero). Determine the angular velocity of C1 when it loses contact with C2.Please answer this fast. Need it for a test tomorrow. Thanks a lot!
 
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  • #2
Please repost this problem in the homework section using the template provided and show us at least some attempt at finding the solution yourself .

Just drawing a diagram would be a good place to start .
 
  • #3
Snehit said:
Please answer this fast. Need it for a test tomorrow.
Hello Snehit, :welcome:

Before a mentor locks the thread (and becasue I do feel sorry for you and I'm such a nice guy :smile: ) : your test is about Lagrangian mechanics ? So (in the PF spirit - for which you have no time through no fault of us) the least you can do is post your Lagrangian and what the Lagrange equations yield from that
 
  • #4
And if you are in a hurry and need a short cut: if the trajectory has to be a circle, a centripetal force is needed. When that force isn't present (not enough of it), it loses contact. Much easier ...

nice exercise ! Kudos for the composer.
 

1. How does friction affect the motion of a cylinder rolling on a fixed cylinder?

Friction between the two cylinders can either slow down or speed up the rolling motion, depending on the direction of the friction force. If the friction force acts in the opposite direction of the cylinder's motion, it will slow down the rolling. If the friction force acts in the same direction as the cylinder's motion, it will speed up the rolling.

2. What is the relationship between the radius of the cylinders and the speed of the rolling motion?

The speed of the rolling motion is directly proportional to the radius of the cylinders. This means that as the radius of the cylinders increases, the speed of the rolling motion also increases. This relationship is known as the rolling motion's angular velocity, which is determined by the ratio of the two cylinders' radii.

3. Can a cylinder ever roll without any slipping on a fixed cylinder?

Yes, a cylinder can roll without slipping on a fixed cylinder if the static friction force between the two cylinders is equal to the maximum possible static friction force. This means that the force of friction is able to provide enough torque to prevent slipping and maintain pure rolling motion.

4. How does the mass of the cylinder affect its rolling motion on a fixed cylinder?

The mass of the cylinder does not affect its rolling motion on a fixed cylinder. This is because the motion of the cylinder is determined by its moment of inertia, which is dependent on the distribution of mass around the axis of rotation, not the total mass of the cylinder.

5. What factors can affect the stability of a cylinder rolling on a fixed cylinder?

The stability of a cylinder rolling on a fixed cylinder can be affected by a few factors, including the height of the center of mass above the ground, the radius of the cylinder, and the coefficient of friction between the two cylinders. A higher center of mass, smaller radius, and lower coefficient of friction can all contribute to a more stable rolling motion, while the opposite can lead to instability and potential tipping.

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