A spherical body moving with an unknown center of mass

[y.moghadamnia]

We have a sphere that its center of mass is not located in its center. suppose it has a mass of m.

what we want to do here is to write its movement equations, using Newton's laws or lagranigian.by move ment we mean writing the equations if a) a force F acts on the body on a surface that is fri?ction-free b) part a, this time with friction. how will the body move? and how can we describe it better

I have solved lots of mechanics problems before, but for this one, I don't know where to start, and how to relate its center of mass to the whole body. should I involve moment of inertia in my equations?

 

[member 553083]

can you help me with this? For the first part, a), you can use Newton's second law of motion to express the equations of motion for the sphere. This involves the force F acting on the body, and the mass m. In this case, the equations of motion would be: F = ma Where 'a' is the acceleration of the sphere. For the second part, b), you can use the same equations of motion, except that this time you need to add a frictional force to the equation. This frictional force would be equal to F_f = - μF_n Where 'μ' is the coefficient of friction, and 'F_n' is the normal force due to gravity acting on the body. In both cases, you do not need to involve the moment of inertia in your equations. However, if you are working with a rotating sphere, then it would be useful to consider the moment of inertia in your equations.