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

• Hajar
In summary, the conversation discusses the use of Newton's second law of motion to demonstrate how the mass of an object affects the rotational motion of a system with a pulley and attached solids. It is suggested to create a free body diagram and solve simultaneous equations to account for the kinematic constraint between linear and rotational motion.
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

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.

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.

## 1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. This type of motion can be observed in objects such as spinning tops, merry-go-rounds, and wheels.

## 2. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

## 3. How is rotational motion different from linear motion?

Rotational motion involves movement around an axis, while linear motion involves movement in a straight line. In rotational motion, the distance from the axis of rotation is important, whereas in linear motion, the distance traveled is important.

## 4. What are the units of torque?

Torque is measured in units of Newton-meters (N·m) in the SI system. In the imperial system, it is measured in foot-pounds (ft·lb).

## 5. How does rotational inertia affect rotational motion?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in rotational motion. Objects with a larger rotational inertia will require more torque to change their rotational speed, while objects with a smaller rotational inertia will require less torque.

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