How Does Mass Affect the Direction of Rotational Motion in a Pulley System?

[Hajar]

Hello
Consider a pulley with a rope winded up around it, and two solids attached to the rope from each side. It is intuitive that the solid with the most mass will impose the direction of the rotational motion of the system ( note that the pulley can rotate), but i'd like to know how can we demonstrate that using Newton's second law of motion.
Thank you

 

[BvU]

Hello Hajar,

Well, first we write down this second law of motion in formula form and then we insert the right values for the various variables. Can you make a start ? Use symbols for the masses and make a diagram of the forces that act.

 

[Dr.D]

Make the drawing first, in what is called Free Body Diagram form (FBD). This will have three parts to show (1) the pulley, the wrapped rope, (2) the greater mass, and (3) the lesser mass. Add to that the direction of the gravity vector.

Then, with that diagram in front of you, write the equation of rotational motion for the pulley and a translational equation of motion for each mass. Solve these equations simultaneously with the kinematic constraint that must exist between the linear motion of the masses and the rotation of the pulley.