Tutor (me) needs help on pulley angular accel question

[Ground State]

I am a high school teacher tutoring a family member in an introductory university class. I have good knowledge of typical pulley questions and semi-decent knowledge of angular acceleration (it is no longer in the high school curriculum here and I am out of practice). Can anyone give me a solution to the following so I can construct the best way to teach it to someone? Solution WILL NOT be simply handed over. The question is asking to solve for the angular acceleration of the cylinders (frictionless).

http://img838.imageshack.us/img838/70/pulley.jpg

 

[Doc Al]

Apply Newton's 2nd law for rotation and for translation. Give it a shot and you'll get plenty of feedback.

As always, start with free body diagrams for each object. You'll need three.

 

[Ground State]

I have no trouble doing a calculation for the angular acceleration of the "big disc" with the 2.5 kg rope hanging off the side, and a calculation for the angular acceleration of the "small disc" with the 4.0 kg mass hanging off the side. But I just can't seem to understand the connection of how this all goes together if the two discs are mounted together as one mass.

 

[Doc Al]

I have no trouble doing a calculation for the angular acceleration of the "big disc" with the 2.5 kg rope hanging off the side, and a calculation for the angular acceleration of the "small disc" with the 4.0 kg mass hanging off the side. But I just can't seem to understand the connection of how this all goes together if the two discs are mounted together as one mass.

It's really the same basic idea. One difference, of course, is that the rotational inertia of the combined mass is the sum of the separate rotational inertias. A second difference is that the ropes attach at different radii.

How would you draw the free body diagrams?

 

[Nickie]

I would suggest approaching this question by first reviewing the basic concepts of pulleys and angular acceleration. This will help you to refresh your own understanding and also provide a solid foundation for teaching the material to your family member.

Next, I would recommend breaking down the problem into smaller, more manageable parts. Start by identifying the forces acting on each cylinder and the pulley system as a whole. This will involve considering the weight of each cylinder, the tension in the rope, and the normal force between the cylinders and the pulley. Draw a free body diagram for each cylinder to help visualize the forces involved.

Then, use Newton's Second Law (F=ma) to write equations of motion for each cylinder in terms of the angular acceleration. Remember that the linear acceleration of each cylinder is related to the angular acceleration by the radius of the cylinder.

Next, consider the relationship between the two cylinders and how their motions are connected. This can be done by applying the principle of conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque.

Finally, solve the system of equations you have created to find the value of the angular acceleration. This may involve substitution and manipulation of equations.

Remember to check your answer for reasonableness and accuracy. If possible, try to come up with multiple ways to solve the problem to provide a deeper understanding for your family member.

In summary, by reviewing the basic concepts, breaking down the problem, and applying relevant principles and equations, you should be able to find a solution to the problem and effectively teach it to your family member. Good luck!