Flywheel of a steam engine problem

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SUMMARY

The problem involves calculating the tangential linear acceleration of a particle located 52.4 cm from the axis of rotation of a flywheel, which operates at a constant angular speed of 156 rev/min and decelerates to rest in 2.20 hours. The angular acceleration, calculated as -1.18 rev/min², is derived from the initial and final angular speeds. The tangential acceleration is then determined using the formula At = r(α). The mention of 72.5 rev/min serves as extraneous information unless radial acceleration is required.

PREREQUISITES
  • Understanding of angular motion and acceleration
  • Familiarity with the concepts of tangential and radial acceleration
  • Knowledge of the relationship between angular velocity and linear velocity
  • Ability to convert units of angular speed (rev/min to rad/s)
NEXT STEPS
  • Learn how to calculate radial acceleration using the formula Ar = ω²r
  • Study the principles of angular deceleration and its effects on rotational systems
  • Explore the relationship between torque, angular acceleration, and moment of inertia
  • Investigate the dynamics of flywheel systems in mechanical engineering applications
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as engineers and mechanics involved in the design and analysis of rotating machinery.

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Homework Statement


The flywheel of a steam engine runs with a constant angular speed of 156rev/min. When the steam is shut off, the friction of the bearings and of the air brings the wheel to rest in 2.20h. What is the tangential linear acceleration of a particle 52.4cm from the axis of rotation when the flywheel is turning at 72.5rev/min.


Homework Equations



At= r(alpha)

I know what the radius is, so I must find angular acceleration.

alpha = (Wf-Wi)/t
_____=(0-156)/(2.2*60)
_____=-1.18rev/min^2

Therefore

At= (52.4cm)(-1.18rev/min^2)


3. The attempt at confusion

So now that I am done, I am left wondering why someone would put 72.5 rev/min in the equation. I was tempted to put that into my equation to find alpha, but then I am lacking time. I then turned towards my linear equivalent equations, but I am lacking time it takes to decelerate to 72.5 or the amount of rotations it takes to get that far. What am i meant to do?
 
Last edited:
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Its not unheard for a problem to contain extraneous information. You've correctly figured that the tangential acceleration is constant and you don't need the speed. If there is a followup question asking you to compute the radial acceleration? Then you will need the speed.
 
Yeah the next one was calculate the total force, so I realized that the speed was simply used in omega^2(r), so that cleared it up. Thanks though, it had me for a bit
 

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