When Does a Disc Reach Its Average Angular Velocity During Each Revolution?

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Homework Help Overview

The discussion revolves around understanding the concept of average angular velocity in the context of a spinning disc. Participants are exploring how to determine the time at which the disc reaches its average angular velocity during each revolution, particularly focusing on the relationship between angular displacement and time.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to define average angular velocity and relate it to angular displacement. There are questions about the relationship between rotation angle and the number of turns, as well as the implications of constant angular acceleration. Some participants suggest specific formulas and explore the definitions of angular measurements.

Discussion Status

The discussion is active, with various participants contributing definitions and attempting to clarify concepts. Some guidance has been offered regarding the relationship between angular displacement and time, but there is no explicit consensus on the correct approach or formula yet.

Contextual Notes

Participants are working within the constraints of a homework assignment that references previous questions and data sets, which may not be fully accessible to all contributors. There is an emphasis on understanding the definitions and relationships involved in angular motion.

Meadow_Lark
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I am so confused by this question. I do not have a clue what I am supposed to do here. Can you please help??

[1pt] For each ith revolution, at what time point does the disc reach its average angular velocity? For example, for the 10th revolution what is the total elapsed time from the beginning of the first revolution to the point in the 10th revolution when the angular velocity of the disc is equal to the average angular velocity you plotted in Q6 for revolution number 10?

Assume that time t=0 at the beginning of the first revolution (i = 1).

Give a formula for this and use your answer in Q8 to guide you. It may help to do this first for the cases (i = 1) and (i = 2), then generalize.

Below are the 2 questions and corresponding answers referenced above.
Q6: Provide a graph of the average angular velocity vs. revolution number for three data sets your group recorded. All data sets should appear on a single graph.

Graph from Q6:

upload_2014-10-22_22-57-41.png


Q 8: In order to find the angular acceleration, we need to make a graph that has angular velocity on the vertical axis and time on the horizontal axis. What we determined before for Q6 was average angular velocity and revolution number. We now need to assign a time value to each average angular velocity point we computed so we can build a new graph of angular velocity vs. time.

Let’s assume that the spinning disc accelerates (or decelerates as the case may be) at a constant rate. For any given revolution, the average acceleration value you plotted for it in Q6 should be reached at:

Answer from Q8:

D) ½ of the way through the revolution
 
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You need to know the definition of angular velocity.

ehild
 
Average angular velocity = ΔΦ/Δt...still doesn't help.
 
How does the rotation angle Φ related to the number of turns?
 
Are you asking me in general or specifically to this question? (in general; 2πr = 1 revolution)
 
I'm pretty sure this is wrong, but... a formula for the time of average angular velocity tωavg = Φ/2
 
Meadow_Lark said:
Are you asking me in general or specifically to this question? (in general; 2πr = 1 revolution)

I ask in general. 2pir is length, not the angle. What is the angle that corresponds to a whole turn?
 
360 degrees
 
Meadow_Lark said:
360 degrees
Yes! and what is it in radians?
 
  • #10
2pi
 
  • #11
Well. So one turn means 2pi radian change of angle. If the angular velocity is ω, what time is needed for one turn?
 

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