How Do Two Connected Discs with Masses Affect Angular Acceleration?

In summary: That might be correct, but I doubt it. Check your signs.Not quite. Your eqn 1 and eqn 2 are only correct if you are taking up as positive everywhere, including the accelerations. The third equation above therefore has both masses accelerating the same way. That might be correct, but I doubt it. Check your signs.Ah I see. I'll double check my signs. Thank you for the help so far. Will post back when I'm done double checking.In summary, the problem involves two discs of radii R and r that are fixed together and rotate together. Strings are wound around both discs and two equal masses M are connected to the ends of the strings. To
  • #1
lmao2plates
14
0

Homework Statement


Two discs of radius R and r are fixed to each other, i.e., they rotate
together. Strings are wound around both discs and two equal masses M
are connected to the ends of the strings (see Figure 1). Find the angular
accelerations of the discs, the accelerations of the masses and indicate
the direction of rotation of the discs (neglect the rotational inertia of the
discs).

http://www.physics.louisville.edu/wkomp/teaching/summer2005/p298/quizzes/quiz4.pdf

The diagram looks like question 3 from above webpage except with the masses being equal.

Homework Equations


at=αr
F=ma

The Attempt at a Solution


[/B]
The problem I have while attempting a solution is that the question tells me to neglect the rotational inertia (moment of inertia). However, if we consider the moment of inertia, it is obvious that the system will rotate to the right since the smaller wheel has a smaller moment of inertia.
 
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  • #2
Why do you have a problem with that? They are just saying to assume the disks have no mass. That kind of assumption if very common in beginning instruction problems such as this.
 
  • #3
phinds said:
Why do you have a problem with that? They are just saying to assume the disks have no mass. That kind of assumption if very common in beginning instruction problems such as this.

So if I assume that the discs have no mass, we are also neglecting the gravity? I think I am missing something here.
I just find it difficult when a question does not give me any quantitative value to work with.

I appreciate your help.
 
  • #4
bump

Here's my working so far:

Angular acceleration is the same for both discs = α
=> acceleration of mass 1 = αR and mass 2 = αr

I then drew free body diagrams of the 2 masses with mass 1 on the left and mass 2 on the right.

Fnet=ma

T1 - Mg = M(a1) - eq.1

T2 - Mg = M(a2) - eq.2

eq1-eq2

T1 - T2 = M(a1-a2) = M(αR-αr)

since R>r, (αR-αr) is > 0 => T1-T2 > 0

therefore T2 < T1 so the system is accelerating to the right.

I am not really sure on this solution.

Could a helper possibly review this for me and suggest the correct approach??
 
  • #5
Bump, I uploaded the full problem in attachemtn
 

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  • #6
Bumping is not allowed on PF.
 
  • #7
lmao2plates said:
So if I assume that the discs have no mass, we are also neglecting the gravity?

No, I don't understand why you would think that. Look, if it makes you happy, then DO consider the mass of the disks and DO take rotational inertia into account. Ignore the fact that the problem statement doesn't tell you the mass of the disks and specifically tells you not to take it into account. I was just trying to help you understand why the problem was stated as it was stated.
 
  • #8
phinds said:
No, I don't understand why you would think that. Look, if it makes you happy, then DO consider the mass of the disks and DO take rotational inertia into account. Ignore the fact that the problem statement doesn't tell you the mass of the disks and specifically tells you not to take it into account. I was just trying to help you understand why the problem was stated as it was stated.

Yea I understand what you mean now. Sorry about that.

The problem I am really facing with this problem as evident by my attempt at the solution in post number 4. The question asks to find the angular acceleration, do I just give it as α? or do I derive that from other variables stated in the problems? There aren't many to begin with either.

Thank you.
 
  • #9
lmao2plates said:
do I derive that from other variables stated in the problems?
Yes.
Consider the FBD of the pair of discs. What torque v. acceleration equation can you write there?
 
  • #10
haruspex said:
Yes.
Consider the FBD of the pair of discs. What torque v. acceleration equation can you write there?

Okay. Torque = Iα. However since we are neglecting the moment of inertia of the discs, torque would be 0?
 
  • #11
lmao2plates said:
Okay. Torque = Iα. However since we are neglecting the moment of inertia of the discs, torque would be 0?
Yes. So what is the net torque in terms of the tensions?
 
  • #12
haruspex said:
Yes. So what is the net torque in terms of the tensions?

net torque = radius * tension

=> 0 = T1R - T2r
=> T1R = T2r
=> T1 = T2(r/R)

so T2(r/R) -T2 = M(αR-αr)
T2(r/R-1) = M(αR-αr)

It seems like I am going in circles haha.
 
  • #13
lmao2plates said:
net torque = radius * tension

=> 0 = T1R - T2r
=> T1R = T2r
=> T1 = T2(r/R)

so T2(r/R) -T2 = M(αR-αr)
T2(r/R-1) = M(αR-αr)

It seems like I am going in circles haha.

EDIT: so from there, assuming that the above equation is valid,

α = T2(r/R-1)/M
 
  • #14
lmao2plates said:
net torque = radius * tension

=> 0 = T1R - T2r
=> T1R = T2r
Yes. You have your original eq 1 and eq 2, plus a relationship between a1 and a2 that you used without stating. You now have four equations and four unknowns.
 
  • #15
haruspex said:
Yes. You have your original eq 1 and eq 2, plus a relationship between a1 and a2 that you used without stating. You now have four equations and four unknowns.

Okay so now I have
T1 - Mg = M(a1)

T2 - Mg = M(a2)

a1/R = a2/r

T1 = T2(r/R)
 
  • #16
lmao2plates said:
Okay so now I have
T1 - Mg = M(a1)

T2 - Mg = M(a2)

a1/R = a2/r

T1 = T2(r/R)
Not quite. Your eqn 1 and eqn 2 are only correct if you are taking up as positive everywhere, including the accelerations. The third equation above therefore has both masses accelerating the same way.
 

1. What is rotational motion problem?

Rotational motion problem is a type of physics problem that involves the study of objects in circular motion. It involves the calculation of various rotational quantities such as angular velocity, torque, and moment of inertia.

2. What is the difference between translational and rotational motion?

Translational motion refers to the movement of an object from one point to another in a straight line, while rotational motion refers to the circular movement of an object around a fixed point.

3. How do you solve a rotational motion problem?

To solve a rotational motion problem, you need to first identify the given parameters such as the radius, angular velocity, and torque. Then, you can use the appropriate formulas and equations to calculate the unknown quantities.

4. What are some real-world applications of rotational motion?

Rotational motion is commonly observed in many everyday objects and activities, such as the spinning of a top, the rotation of a wheel, the movement of a fan, and the swinging of a pendulum. It is also essential in understanding the motion of planets and other celestial bodies.

5. How does rotational motion relate to angular momentum?

Angular momentum is a quantity that describes the rotational motion of an object. It is defined as the product of an object's moment of inertia and its angular velocity. Therefore, rotational motion is closely related to angular momentum, and changes in one can affect the other.

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