Angular velocity of a solid disk

In summary, the conversation discusses the problem of a solid disk spinning at an angular velocity of 35.0 rad/s, with a mass of 3.6kg and a radius of .50m. A thin ring with the same radius and mass is then dropped onto the disk, and the conversation discusses how to calculate the final angular velocity of the disk and ring together. The equation used is L_i=L_f, where L represents angular momentum, I represents rotational inertia, and ω represents angular velocity. The final equation to solve for the final angular velocity is (.45)(35m/s)=(.45+.90)(W_f).
  • #1
Nininguyen6
9
0

Homework Statement



A solid disk is spinning around it center with an angular velocity of 35.0 rad/s. The disk has a mass of 3.6kg and a radius of .50m. You drop a thin ring with the same radius and a mass on the disk along the same center of rotation. What is the angular velocity of the disk and ring?

Homework Equations


Id= 1/2mR^2
Ir=mR^2
w=vf/R


The Attempt at a Solution



Id=1/2(3.6kg)(.50)^2 =.45 kg m/s
Ir= (3.6)(.50)^2= .90

W= (I'd+Ir)/ R
= (.45+.90)/(.50)
=2.7 rad/s

Is that the correct answer?
 
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  • #2
Nininguyen6 said:

Homework Equations



w=vf/R

w stands for angular velocity right?

That's the relationship between linear velocity (at a distance R) and angular velocity.
For this problem you'll want to use conservation of angular momentum.
 
  • #3
Would it be Li=Lf= i(wf)
 
  • #4
Yes, it would be [itex]L_i=L_f[/itex] (initial angular momentum = final angular momentum)

So what is the initial angular momentum? What then changes? And what does this change do to the angular velocity?
 
  • #5
The initial is 35 rad/s aNd nothing changes because the second object is has the same mass and radius. Therefore would the finial be 35 as well?
 
  • #6
35 rad/s is the initial angular velocity, but it is not the same as the initial angular momentum.

Angular momentum is conserved, not angular velocity.
 
  • #7
So it would be L= I times w

Since I solved for IDisk and Iring, would I add those two up and mutiple by w?
 
  • #8
What would be your reasoning for doing that?

You know [itex]I_i[/itex] and [itex]ω_i[/itex] and [itex]I_f[/itex] so how can you solve for [itex]ω_f[/itex]?


(Check posts #3 and #4)
 
  • #9
((Id)(wd)+(Ir)(wr)) / R
= answer

Wf=w initial - answer
And that would give me the final angular vel?
 
  • #10
Nininguyen6 said:
((Id)(wd)+(Ir)(wr)) / R
= answer

Wf=w initial - answer
And that would give me the final angular vel?

I'm not sure where you're getting these equations.

If:
[itex]L_i=L_f[/itex]

Then:
[itex]I_iω_i=I_fω_f[/itex]So what is the final rotational inertia?
 
  • #11
I'm a little confused because I solved for the iRing and the iDisk but no I don't know where to plug it in
 
  • #12
iDisk is the initial rotational inertia right?

And after the ring is added, it still has that initial rotational inertia, but now it also has an additional rotational inertia from the ring (iRing)

How would you write that in math?
 
  • #13
So would it be (.45)(2.7rad/s)=(.45+.90)(Wf)?
 
  • #14
Nininguyen6 said:
So would it be (.45)(2.7rad/s)=(.45+.90)(Wf)?

Very close, but where did you get 2.7 rad/s?
 
  • #15
I got 2.7 from the first post so would it be (.45)(35m/s)=(.45+.90)(Wf)?
 
  • #16
Yes, it would be that.

Now just solve for the final angular velocity and you're done!
 
  • #17
THANK YOU! Very much appreciated Nathanael
 
  • #18
No problem, and welcome to the physics forums!
 

1. What is angular velocity of a solid disk?

Angular velocity of a solid disk is the rate of change of the angle between any two radial lines on the disk, measured in radians per unit time.

2. How is angular velocity of a solid disk measured?

Angular velocity of a solid disk can be measured by dividing the change in angle by the change in time. It is typically represented by the symbol "ω" and has units of radians per second (rad/s).

3. What factors affect the angular velocity of a solid disk?

The angular velocity of a solid disk can be affected by the radius of the disk, the torque applied to the disk, and the distribution of mass within the disk. Other factors such as friction and air resistance may also have an impact.

4. How does angular velocity relate to linear velocity?

Angular velocity and linear velocity are related through the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius of the disk. This relationship shows that as the radius increases, the linear velocity also increases for a given angular velocity.

5. How is the direction of angular velocity determined?

The direction of angular velocity is determined by the right-hand rule, which states that if the fingers of the right hand are curled in the direction of rotation, then the thumb points in the direction of the angular velocity vector. This rule applies for both clockwise and counterclockwise rotations.

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