What is the angular velocity at t = 2.4 sec based on given graph?

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Homework Help Overview

The discussion revolves around determining the angular displacement of a rotating wheel at a specific time (t = 2.4 seconds) based on a provided graph of angular velocity as a function of time. Participants are analyzing the relationship between angular velocity, angular acceleration, and displacement in the context of rotational motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to calculate angular displacement using equations of motion, questioning the accuracy of their calculated angular acceleration and the values derived from the graph. Some suggest using the area under the curve of the graph to find displacement, while others raise concerns about the assumptions made regarding the values at specific times.

Discussion Status

The discussion is ongoing, with participants providing different methods and questioning the assumptions behind their calculations. Some guidance has been offered regarding the interpretation of the graph and the relationship between angular velocity and displacement, but no consensus has been reached on the correct approach.

Contextual Notes

Participants are working with a graph that shows angular velocity over time, and there are discussions about the implications of constant acceleration and the choice of reference points for calculations. There is an acknowledgment of potential errors in initial calculations and the need for clarification on how to interpret the graph accurately.

SalsaOnMyTaco
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Homework Statement


The graph shows the angular velocity of a rotating wheel as a function of time.
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1201/summer/homework/Ch-10-Rotation/ang_vel_graph/omega_vs_t-2.jpg

What is the angular displacement of the wheel at t = 2.4 sec?

Homework Equations


ωf=ωi+αt

θ=θ0+ωit+1/2αt2


The Attempt at a Solution


I first try to find the acceleration it takes from initial angular velocity to move to t=2.4s
-6=-9+a(2.4)=1.25
α=1.25

so assuming θ0=0

θ=-9(2.4)+1/2(1.25)(2.4)2
θ=-18?
 
Last edited by a moderator:
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any ideas? i also tried W=θ/t
 
what about bxh/2= 2.4*-6/2=-7.2 since the θ is the area is between above the line and the horitzonal x
 
SalsaOnMyTaco said:

Homework Statement


The graph shows the angular velocity of a rotating wheel as a function of time.
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1201/summer/homework/Ch-10-Rotation/ang_vel_graph/omega_vs_t-2.jpg

What is the angular displacement of the wheel at t = 2.4 sec?

Homework Equations


ωf=ωi+αt

θ=θ0+ωit+1/2αt2


The Attempt at a Solution


I first try to find the acceleration it takes from initial angular velocity to move to t=2.4s
-6=-9+a(2.4)=1.25
α=1.25

so assuming θ0=0

θ=-9(2.4)+1/2(1.25)(2.4)2
θ=-18?

Your calculated angular acceleration is wrong. The angular velocity at time zero is -9 rad/s, and it is zero at time 6 seconds. So it increases by 9 rad/s over a time interval of 6 seconds.
 
Last edited by a moderator:
Chestermiller said:
Your calculated angular acceleration is wrong. The angular velocity at time zero is -9 rad/s, and it is zero at time 6 seconds. So it increases by 9 rad/s over a time interval of 6 seconds.
Thanks,
but shouldn't my final angular velocity be -6 since its asking for the displacemente at 2.4s?
 
SalsaOnMyTaco said:
Thanks,
but shouldn't my final angular velocity be -6 since its asking for the displacemente at 2.4s?

It is a constant acceleration. Which means Δv/Δt is constant. You can take any points as values.
The problem is that you are taking velocity at time of 2.4 secs.
You can only get approximate value of v at 2.4 sec from the graph.

Rather than taking value of velocity at 2.4sec, why not use other values that easy and accurate to calculate. It does not matter where you get your Δv and Δt since it is a linear function.
 

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