Rotational Motion of a wheel turning

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Homework Help Overview

The discussion revolves around a problem in rotational motion, specifically involving a wheel that accelerates from rest at a specified rate. Participants are tasked with determining the time taken to complete a certain number of revolutions and the corresponding rotational speed.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to convert angular acceleration from radians to revolutions and seeks guidance on the next steps. Some participants suggest using standard equations for constant angular acceleration and emphasize the importance of unit consistency.

Discussion Status

Participants are actively engaging with the problem, offering suggestions for unit conversions and the application of relevant equations. There is a focus on ensuring that all units are compatible before proceeding with calculations.

Contextual Notes

There is a mention of the need to convert revolutions to radians for accurate calculations, as well as a reminder about the importance of maintaining proper unit spacing in expressions.

Falinox
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Homework Statement


A wheel starting from rest accelerates at 1.2 rad/s² counterclockwise.
A) How long does it take to turn through 60 revolutions?
B)What is the rotational speed at that time?

2. The attempt at a solution

I converted 1.2rad/s² to 1.885 rev/s² by dividing by 2πrad (2 pi radians).
So where can I go from here?

Once I find the time in part A I can use the fact that ω=Δθ/ΔT to find the "rotational speed" correct?
 
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Welcome to PF!

Hi Falinox! Welcome to PF! :wink:
Falinox said:
I converted 1.2rad/s² to 1.885 rev/s² by dividing by 2πrad (2 pi radians).
So where can I go from here?

Once I find the time in part A I can use the fact that ω=Δθ/ΔT to find the "rotational speed" correct?

(btw, always leave a space between the number and the unit)

No, you need to use the standard constant acceleration equations, using angular displacement speed and acceleration instead of the linear versions. :smile:
 
and i suggest you use radians rather than revolutions; the equations look much nicer that way.
 


tiny-tim said:
Hi Falinox! Welcome to PF! :wink:(btw, always leave a space between the number and the unit)

No, you need to use the standard constant acceleration equations, using angular displacement speed and acceleration instead of the linear versions. :smile:


Thanks for the reply!

ω²=ω₀²+2αθ
Given: ω₀=0 rad/s, α=1.2 rad/s²

Is θ my 60 rev? (maybe convert 60 rev to rad?)
 
that is the right idea, and yes, theta=60rev, but make sure your units all match before plugging things in. your formula is only true if you use radians, so i would recommend that.
 

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