How to Account for Rotational Motion in a Pulley Problem?

The correct answer takes into account the moment of inertia of the hoops, which is given by I = MR^2. Using this, the correct answer for the tension is t = g(M1M2)/(M1 + M2 + (M1R1^2 + M2R2^2)/R^2). In summary, the problem is a variation of Atwood's machine and the correct expression for tension takes into account the moment of inertia of the hoops. The answer given by neglecting the rotational motion is incorrect as it assumes the hoops are pointlike.
  • #1
danny271828
34
0
A massless string is placed over a massless pulley, and each end is wound around and fastened to a vertical hoop. The hoops have masses M1 and M2 and radii R1 and R2. The apparatus is placed in a uniform gravitation field g and released with each end of the string aligned along the field.



I have to show that the tension is t = gM1M2/(M1+M2)



I keep getting twice this value.
 
Physics news on Phys.org
  • #2
  • #3
danny271828 said:

I keep getting twice this value.

You are getting twice of the value, because you are neglecting the rotational motion of the hoops. The answer you got (twice value) is in the case when hoops are pointlike.
 

FAQ: How to Account for Rotational Motion in a Pulley Problem?

What is a pulley problem?

A pulley problem is a physics problem that involves calculating the forces and motion of objects connected by a pulley system. These problems usually require knowledge of basic mechanics and Newton's laws of motion.

What makes pulley problems difficult?

Pulley problems can be difficult because they involve multiple objects, each with its own forces and motion, connected by a complex system of ropes or cables. It can be challenging to keep track of all the different forces and to properly apply Newton's laws.

What are some tips for solving pulley problems?

It is helpful to draw a diagram of the pulley system and label all the forces acting on each object. Then, use Newton's laws to write equations for each object and solve them simultaneously to find the unknown quantities.

Are there any shortcuts or tricks for solving pulley problems?

One trick for solving pulley problems is to treat the pulley as a massless and frictionless object, which simplifies the calculations. Also, when solving for the tension in ropes, remember that the tension is the same throughout the entire rope.

What applications do pulleys have in real life?

Pulleys are used in many real-life applications, such as elevators, cranes, and zip lines. They are also commonly used in simple machines, like a bicycle, to make it easier to lift or move heavy objects by reducing the amount of force needed.

Similar threads

How Do You Derive the Tension in a Classical Physics Pulley Problem?
Replies
4
Views
18K
Newton's Second Law (Pulley Sustem)
Replies
3
Views
1K
3 pulley problem with attached masses
Replies
15
Views
3K
How Do You Calculate Tensions and Accelerations in a Modified Atwood Machine?
Replies
1
Views
2K
Finding hamiltonian for spring/pulley problem
Replies
1
Views
3K
Two blocks, a fixed pulley and friction
Replies
4
Views
2K
Pulleys with Strings Having Mass
Replies
4
Views
2K
Solving a Tricky Physics Pulley Problem: Finding M2 with Tension and Mass M1
2
Replies
37
Views
3K
Rotation dynamics pulley concept confusion
Replies
4
Views
1K
Pulley attached to a pulley - Find the balance equation
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top