Morin classical mechanics page 326 example

[almarpa]

Homework Statement

A string wraps around a uniform cylinder of mass M, which rests on a fixed plane with angle θ. The string passes up over a massless pulley and is connected to a mass m. Assume that the cylinder rolls without slipping on the plane, and that the string is parallel to the plane. What is the acceleration of the mass m?

Homework Equations

In the solucion, Morin claims that the masses acceleratins are not the same, and they are related by a2=2 a1, where a1 is the acceleratin for M, and a2 the acceleration for m

The Attempt at a Solution

When solving the problem, I used the same value for both accelerations, that is, a1=a2=a, so my result was wrong. Why are the accelerations different, if the pulley is at rest? Where does the a2=2 a1 equation come from?

Regrads.

 

[Vibhor]

Homework Statement

A string wraps around a uniform cylinder of mass M, which rests on a fixed plane with angle θ. The string passes up over a massless pulley and is connected to a mass m. Assume that the cylinder rolls without slipping on the plane, and that the string is parallel to the plane. What is the acceleration of the mass m?

Homework Equations

In the solucion, Morin claims that the masses acceleratin are not the same, and they are related by a2=2 a1, where a1 is the acceleratin for M, and a2 the acceleration for m

The Attempt at a Solution

When solving the problem, I used the same value for both accelerations, that is, a1=a2=a, so my result was wrong. Why are the accelerations different, if the pulley is at rest? Where does the a2=2 a1 equation come from?

Regrads.

When a cylinder/sphere rolls without slipping on a surface ,what is the relationship between velocity of topmost point and velocity of the Center of Mass ?

 

[almarpa]

Yes, I know that the speed in the top is twice the speed of the center of mass, so the accelerations must obey the same relation . This is what Morin suggest to get this equation, altought I have not found the proof for this relation, so I would have never tought of this possibility. I was wondering if this constraint equation can be derived from the "conservation" of the length of the string, as Kleppner - Kolenkow textbook usually does.