What is the Moment of Inertia of a Pulley with Connected Masses?

AI Thread Summary
The discussion focuses on calculating the moment of inertia (I) of a pulley connected to two masses, M1 and M2, with given values and acceleration. The user expresses uncertainty about how to approach the problem and questions the effects of a massless pulley on the system's acceleration. Key concepts include the relationship between torque, moment of inertia, and angular acceleration, as well as the importance of drawing Free Body Diagrams for each mass and the pulley. Participants suggest writing equations of motion for both masses and the pulley to derive the necessary relationships for solving the problem. The conversation emphasizes the need for a systematic approach to understand the dynamics involved.
wesDOT
Messages
28
Reaction score
0

Homework Statement


A mass (M1 = 5.0 kg) is connected by a light rope to a mass (M2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 meter) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s2. What is the moment of inertia of the pulley?

https://ce.byu.edu/courses/univ/694820121006/media/l10g8.gif


Homework Equations



I=mr^2


The Attempt at a Solution



I have no references in my textbook as to how to approach this sort of problem. I'm not sure where I should even begin.
 
Physics news on Phys.org
What would be the acceleration of the system if the pulley was massless?

They give you what the actual acceleration is, so how would you go about accounting for the difference?
 
Couple hints...

Is it fair to say that the pulley has a tangential acceleration equal to the acceleration of the system? (consisting of M1 and M2)

What is the force making the pulley rotate, and how large is it?

M=Ja

Where M is the torque, J is the moment of inertia and a is the angular acceleration
 
It would help to start by drawing a Free Body Diagram (FBD) for each of the masses and the pulley. Then write the equations of motion for each body - two linear equations and one rotational equation, along with the necessary kinematic relations. At that point, it should all be evident how to put it together to find the MMOI of the pulley.
 
I apologize for the late reply. All of what you have said has helped me. Thank you very much. All of you.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is（Figure 2）： F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

What is the "r" in the moment of inertia?
Replies
13
Views
2K
Moment of Inertia with pulley and two masses on a string (iWTSE.org)
Replies
8
Views
12K
Newton's Second Law (Pulley Sustem)
Replies
3
Views
2K
Moment of inertia of a system of masses
Replies
10
Views
2K
Olympiad dynamics problem with 3 masses and a pulley
Replies
17
Views
2K
What Happens to Angular Acceleration and Moment of Inertia in a Pulley System?
Replies
2
Views
7K
Moment of Inertia in Planet System
Replies
9
Views
2K
Angular acceleration of an atwood pulley
Replies
8
Views
4K
Question regarding block and pulley system with inertia
Replies
4
Views
2K
Need help with moment of inertia question
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top