What Is Gaetan Boucher's Total Acceleration at 1/4 Lap?

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Homework Help Overview

The problem involves calculating the total acceleration of Gaetan Boucher as he skates around a circular track with a radius of 100m, starting from rest and increasing his speed uniformly to complete a lap in 30 seconds. The focus is on determining the acceleration at the point that is one-quarter of the way around the track.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the need to calculate both tangential and radial accelerations, with some suggesting methods to find the speed at the quarter lap point. There are inquiries about angular acceleration and its relation to tangential acceleration.

Discussion Status

Participants are exploring various methods to derive the necessary components of acceleration. Some have provided calculations for tangential acceleration, while others are questioning the assumptions made regarding time and angular velocity. There is an ongoing dialogue about the relationship between the tangential and centripetal components of acceleration.

Contextual Notes

There is confusion regarding the time taken to reach the quarter lap mark, with some participants suggesting that the time may be longer than initially calculated. The discussion includes references to the angular acceleration based on the entire lap rather than just the quarter lap.

  • #31
Lolagoeslala said:
i am abit confused
Confused about what in particular ?
 
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  • #32
SammyS said:
Confused about what in particular ?


ωf = 2ωavg = 2(2π)/30 .

Angular acceleration, α = (ωf-0)/30 . That's 1/4 of the former answer.
 
  • #33
Lolagoeslala said:
ωf = 2ωavg = 2(2π)/30 .

Angular acceleration, α = (ωf-0)/30 . That's 1/4 of the former answer.

What you didn't include from that post was:
Base the angular acceleration on one complete lap.
All I did in the above QUOTE'ed text was to repeat what we had previously done, but used a complete lap since for a complete lap, we know the elapsed time. Once you have this value, you will need to find the velocity at the 1/4 lap point so that you can recalculate the radial component of acceleration, since that is also wrong.

Do you know the kinematic equations for constant angular acceleration?




If you work everything out, you would find that using our previous answer for angular acceleration, π/7.5/7.5, one lap would take only 15 seconds.
 
  • #34
SammyS said:
What you didn't include from that post was:
Base the angular acceleration on one complete lap.
All I did in the above QUOTE'ed text was to repeat what we had previously done, but used a complete lap since for a complete lap, we know the elapsed time. Once you have this value, you will need to find the velocity at the 1/4 lap point so that you can recalculate the radial component of acceleration, since that is also wrong.

Do you know the kinematic equations for constant angular acceleration?




If you work everything out, you would find that using our previous answer for angular acceleration, π/7.5/7.5, one lap would take only 15 seconds.


i do not know how to find the
constant angular acceleration
 
  • #35
i am getting 4.60
 
  • #36
Lolagoeslala said:
i am getting 4.60
Yes.

Notice, that's 2/4 of your previous answer. :smile:
 

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