Find the critical rotation rate

In summary: So if we have a net normal force of zero, we can say that the body has no weight.In summary, the tumbler in an upright clothes dryer has a critical angular velocity that causes clothes to experience weightlessness. The radius of the drum is 0.30 m. The critical rotation rate can be expressed in both radians per second and revolutions per minute (RPM). At this rate, the apparent gravity felt by the clothes when passing over the bottom is zero, indicating a net normal force of zero.
  • #1
Milotoadfoot
4
0

Homework Statement



The tumbler in an upright clothes dryer rotates at a critical angular
velocity so that clothes passing over the top briefly experience weightlessness.
If the radius of the drum is 0.30 m, what is this critical rotation rate? (Express
your answer in both radians per second and revolutions per min (RPM).) At
this rate, what is the apparent gravity felt by the clothes when they pass over
the bottom? (Express your answer in multiples of g.)

Homework Equations



arad=v2/R

The Attempt at a Solution


I don't see how we can extrapolate a critical rotation rate from the given equation. Maybe I am just missing something or are we looking for Vf?
 
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  • #2
Consider what the term "weightlessness" means and implies with regards to net acceleration.
 
  • #3
You'll need the angular velocity for the answer, but you can start with the velocity if you like.
There is no need to extrapolate anything. When do you get weightlessness?
 
  • #4
You get weightlessness when g=0
 
  • #5
Milotoadfoot said:
You get weightlessness when g=0

But g is not zero. It's a constant 9.8 m/s2. What other acceleration is in play? What's the net acceleration?
 
  • #6
Well we care about the acceleration of ω right?
 
  • #7
ω is constant, there is no "acceleration of ω". There is an acceleration that has a relation to ω, yes.
 
  • #8
Perhaps "weight" can be thought of as normal force exerted on the body.
 

1. What is the "critical rotation rate"?

The critical rotation rate, also known as the critical angular velocity, is the minimum speed at which a rotating body begins to experience significant changes or deformations in its shape and structure. It is a key parameter in understanding the stability and behavior of rotating systems.

2. How do you calculate the critical rotation rate?

The critical rotation rate can be calculated using various equations and formulas, depending on the specific system and its properties. In general, it takes into account factors such as the mass, size, and shape of the rotating body, as well as the material it is made of and the forces acting upon it. A detailed analysis and understanding of the specific system is necessary in order to accurately calculate the critical rotation rate.

3. Why is the critical rotation rate important?

The critical rotation rate is important because it helps us understand the behavior and stability of rotating systems. It is a crucial factor in designing and engineering structures such as bridges, wind turbines, and aircraft, as well as in studying natural phenomena such as the rotation of planets and stars. It also plays a significant role in determining the maximum safe speed for rotating machinery and equipment.

4. Can the critical rotation rate be exceeded?

Yes, the critical rotation rate can be exceeded, but it can lead to significant changes and deformations in the rotating body. Exceeding the critical rotation rate can cause the body to lose its stability and potentially lead to failure or damage. It is important to carefully consider and understand the critical rotation rate in order to prevent such situations.

5. How does the critical rotation rate affect different materials?

The critical rotation rate can vary depending on the material of the rotating body. Certain materials may have a higher resistance to deformation, allowing them to withstand higher rotation rates before reaching their critical point. Other materials may have a lower critical rotation rate, meaning they are more prone to changes and deformations at lower speeds. The material properties must be taken into consideration when analyzing and calculating the critical rotation rate of a system.

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