Angular Acceleration: Homework Equations & Solution

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Homework Help Overview

The discussion revolves around a problem involving angular acceleration and the number of revolutions made by a wheel that slows down uniformly. The wheel has a diameter of 26.0 inches and starts at a speed of 210.0 revolutions per minute, coming to rest in 15.0 seconds.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the calculation of angular acceleration and the total number of revolutions during the deceleration period. There are attempts to apply different equations, with some questioning the validity of the results based on the wheel's slowing motion.

Discussion Status

The discussion is active, with participants providing various calculations and questioning the assumptions made in the original poster's approach. Some participants suggest checking units and using alternative equations to verify results.

Contextual Notes

There are concerns about the consistency of units used in calculations, particularly regarding the time variable and its impact on the results. Participants are also examining the implications of the wheel making more revolutions while slowing down than it would at its initial speed.

Mowgli
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Homework Statement



A 26.0 in diameter wheel is rotation initially at 210.0 revolutions per minute. It slows down uniformly and comes to rest in 15.0 seconds.

a.) what is the angular acceleration?
b.) through how many revolutions did it turn in those 15.0s?



Homework Equations





The Attempt at a Solution



a.)

f= 210.0 / 60s = 3.5 Hz

ang. accel= 2(pi)f= 2(pi) x 3.5
= 21.99 rad/s

21.99 / 15.0 = 1.47 rad/s^2

b.) 1/2(210 + 0)(15.0)
= 1/2(3150)
= 1575
= 1.60 x 10^3 rev

Can anyone confirm?
 
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Mowgli said:

Homework Statement



A 26.0 in diameter wheel is rotation initially at 210.0 revolutions per minute. It slows down uniformly and comes to rest in 15.0 seconds.

b.) 1/2(210 + 0)(15.0)
= 1/2(3150)
= 1575
= 1.60 x 10^3 rev

Can anyone confirm?
There is a problem here your wheel is slowing down but makes more revolutions in 15s then in a min at the initial velocity.What equation are you using there ?
 
for b.) i was using theta = 1/2(initial velocity + final velocity) x time
 
Mowgli said:
b.) 1/2(210 + 0)(15.0)
= 1/2(3150)
= 1575
= 1.60 x 10^3 rev

Check your units. You should not use t=15s. Your units must be consistent.
 
Mowgli said:


f= 210.0 / 60s = 3.5 Hz



so 1/2(3.5 + 0) (15)
= 1/2 (52.5)
= 26.25 rev
 
Now use another equation to check your answer.
 

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