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

In summary, the conversation discusses finding the time point for the disc to reach its average angular velocity for a given revolution, assuming constant acceleration. This involves assigning a time value to each average angular velocity point and using the formula ωavg = ΔΦ/Δt. The angle for one turn is 2π radians and the time needed for one turn is 1/ω.
  • #1
Meadow_Lark
8
0
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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  • #2
You need to know the definition of angular velocity.

ehild
 
  • #3
Average angular velocity = ΔΦ/Δt...still doesn't help.
 
  • #4
How does the rotation angle Φ related to the number of turns?
 
  • #5
Are you asking me in general or specifically to this question? (in general; 2πr = 1 revolution)
 
  • #6
I'm pretty sure this is wrong, but... a formula for the time of average angular velocity tωavg = Φ/2
 
  • #7
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?
 
  • #8
360 degrees
 
  • #9
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?
 

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

What is average angular velocity?

Average angular velocity is a measure of how fast an object rotates over a certain amount of time. It is calculated by dividing the change in angular displacement by the change in time.

How is average angular velocity different from linear velocity?

While linear velocity measures the rate of change in position of an object in a straight line, average angular velocity measures the rate of change in angular displacement of an object as it rotates around an axis.

Can average angular velocity be negative?

Yes, average angular velocity can be negative if the object is rotating in the opposite direction than the chosen positive direction. The sign indicates the direction of rotation, not the magnitude.

What units is average angular velocity measured in?

Average angular velocity is typically measured in radians per second (rad/s) or degrees per second (°/s). These units represent the amount of rotation per unit of time.

How is average angular velocity used in real life?

Average angular velocity is used in many real-life applications, such as in the design of machinery and vehicles that involve rotational motion, in the study of celestial bodies and their orbits, and in sports such as figure skating and gymnastics. It is also an important concept in physics and engineering, and is used to calculate other parameters like angular acceleration and torque.

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