What is the final angular velocity when two rotating disks are pushed together?

In summary: When the two disks are pushed into each other, their moments of inertia combine and the resulting angular velocity is given by the equation I1ω1 + I2ω2 = (I1 + I2)ωc. In this case, since ω1 = ω and ω2 = ω/2, we can solve for ωc to get our final answer. In summary, the angular velocity of the larger disk when both are rotating together is ωc = 2ω/3.
  • #1
duplaimp
33
0

Homework Statement


Two disks are rotating about an axis common to both. The first disk has moment of inertia I and angular velocity ω. The second disk has moment of inertia 2I and angular velocity [itex]\frac{ω}{2}[/itex]
Both rotate in same direction
If both disks are pushed into each other what is the angular velocity of the larger disk when both are rotating together?

xa9TyS2.png


The Attempt at a Solution


I don't know how to solve this.
I was thinking in [itex]I+2I = \frac{ω}{2} + ω[/itex] but that doesn't make sense.
Any idea in how to start solving this?
 
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  • #2
duplaimp said:

Homework Statement


Two disks are rotating about an axis common to both. The first disk has moment of inertia I and angular velocity ω. The second disk has moment of inertia 2I and angular velocity [itex]\frac{ω}{2}[/itex]
Both rotate in same direction
If both disks are pushed into each other what is the angular velocity of the larger disk when both are rotating together?

xa9TyS2.png


The Attempt at a Solution


I don't know how to solve this.
I was thinking in [itex]I+2I = \frac{ω}{2} + ω[/itex] but that doesn't make sense.
Any idea in how to start solving this?

Conservation of angular momentum.
 
  • #3
[1/2 Iω^2]1 + [1/2 Iω^2]2 = 1/2 (I1 + I2)ωc^2
Where ωc is the common angular velocity
 
  • #4
siddharth23 said:
[1/2 Iω^2]1 + [1/2 Iω^2]2 = 1/2 (I1 + I2)ωc^2
Where ωc is the common angular velocity

EDIT:
this is not conservation of angular momentum. It's an energy equation which is invalid since heat is dissipated when the two disks conjoin.
 
Last edited:
  • #5
rude man said:
EDIT:
this is not conservation of angular momentum. It's an energy equation which is invalid since heat is dissipated when the two disks conjoin.

Oh my bad. That's a very specific case. Sorry.

I1ω1 + I2ω2 = (I1 + I2)ωc
 
  • #6
siddharth23 said:
Oh my bad. That's a very specific case. Sorry.

I1ω1 + I2ω2 = (I1 + I2)ωc

That is correct.
 

What is angular velocity and how is it different from linear velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed axis. It is different from linear velocity, which is a measure of how fast an object is moving in a straight line. Angular velocity is typically measured in radians per second, while linear velocity is measured in meters per second.

How is the angular velocity of two disks calculated?

To calculate the angular velocity of two disks, you need to know the angular displacement and time taken for the disks to rotate. The formula for angular velocity is angular displacement divided by time, or ω = Δθ/Δt. The units for angular displacement are radians and the units for time are seconds.

What factors affect the angular velocity of two disks?

The angular velocity of two disks can be affected by several factors, including the size and mass of the disks, the distance between the two disks, and the force applied to them. Other factors that can affect angular velocity include friction, air resistance, and the shape of the disks.

How does the direction of rotation affect the angular velocity of two disks?

The direction of rotation does not affect the angular velocity of two disks. Angular velocity is a measure of how fast an object is rotating, regardless of the direction of rotation. However, the direction of rotation can affect other factors, such as the torque and angular momentum of the disks.

What are some real-world applications of understanding the angular velocity of two disks?

Understanding the angular velocity of two disks can have practical applications in many industries, such as in manufacturing and engineering. It can help in designing and optimizing rotating machinery, such as car engines and turbines. It is also useful in understanding the motion of celestial bodies, such as planets and galaxies. Additionally, understanding angular velocity can aid in sports science, such as in analyzing the movements of athletes in sports like gymnastics and figure skating.

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