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

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Gaetan Boucher skated around a circular track with a radius of 100m, completing a lap in 30 seconds while accelerating from rest. To find his total acceleration at the 1/4 lap mark, the tangential and radial components of acceleration must be calculated separately, as they are perpendicular vectors. The tangential acceleration was determined to be 5.58 m/s², while the centripetal acceleration was calculated based on his speed at that point. After resolving the components, the total acceleration magnitude was found to be approximately 18.38 m/s², although discrepancies in time calculations led to confusion regarding the correct answer options. Ultimately, the discussion emphasized the importance of correctly applying angular acceleration formulas and kinematic equations.
  • #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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