Rotational Kinematics (String attached to disk)

[mattj150]

Homework Statement

Determine the relationship between the angular
acceleration of the flywheel, the downward acceleration of the block, and the radius of
the ring.

Known data:
Mass Ring: 1.420 kg
Radius Ring (Inside, then Outside): 5.10 cm, 6.325 cm
Mass Disk: 1.455 kg
Radius Disk: 11.45 cm
Mass Shaft: Negligable
Radius Shaft: 0.6 cm

Homework Equations

ω=ω0 + αt
f=ma

The Attempt at a Solution

I'm really lost on this, i assume that i need to calculate the tension the block places on the string (F=MA)? Could anyone give me a hint on how to get started on this.

 

[Simon Bridge]

Welcome to PF;
Your wish is my command:
hint: draw free-body diagrams.

Though you could use conservation of energy and assume acceleration is constant.

 

[mattj150]

I understand how to do the FBD for the hanging mass. The forces acting on it are simply Fg and Ft. How would i do a FBD for the spinning mass? Would i pick a point on the outer edge to do it for?

 

[Simon Bridge]

The tension force acts at a particular location on the flywheel - creating a torque. ##\tau=I\alpha##

 

[Nickie]

I would approach this problem by first identifying the relevant equations and variables. In this case, we are dealing with rotational kinematics, so we can use the equation ω=ω0 + αt, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time.

Next, we can consider the forces acting on the system. The block is accelerating downward, so there must be a force pulling it in that direction. This force is provided by the tension in the string, and we can use the equation f=ma to relate the force to the mass and acceleration of the block.

To determine the relationship between the angular acceleration and the downward acceleration of the block, we can use the fact that the string is attached to the disk, which is rotating. This means that the string is also experiencing a rotational motion, and the angular acceleration of the disk will be related to the downward acceleration of the block.

Finally, we can use the given masses and radii to calculate the moment of inertia of the system, which is needed to fully describe the rotational motion.

Overall, the key to solving this problem is to carefully consider the forces and motions involved, and use the relevant equations to relate them.