Calculating Revolutions for a Spinning Wheel | Circular Motion Problem

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Homework Help Overview

The problem involves calculating the number of complete revolutions made by a wheel spinning at a constant angular speed of 2.50 rad/s over a duration of 30.0 seconds. Participants are exploring concepts related to circular motion and angular displacement.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants attempt to apply angular motion equations but express confusion regarding their calculations and the expected answers. Others question the relationship between radians and complete revolutions, seeking clarification on conversions between these units.

Discussion Status

The discussion reveals a mix of attempts to solve the problem and inquiries about fundamental concepts, such as the conversion of radians to degrees and revolutions. Some participants have provided partial calculations, while others are still seeking foundational knowledge to proceed.

Contextual Notes

There is a noted lack of information regarding angular acceleration, as the wheel is stated to be rotating at a constant speed. Some participants express uncertainty about the conversion processes necessary for solving the problem.

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Homework Statement


A wheel spins at an angular speed of 2.50 rad/s for a total of 30.0s. How many complete revolutions will the wheel make during this time?
A) 31.4 rev
B) 19.3 rev
C) 11.9 rev
D) 75.0 rev

Homework Equations


W=Wo+(alpha)(t)
θ=θo+Wot+1/2(alpha)t^2
W^2=Wo^2+2(alpha)(θ-θo)

The Attempt at a Solution


W=Wo+(alpha)t
2.5rad/s=(alpha)(30s)
Alpha=0.083

W^2=Wo^2+2(alpha)(θ-θo)
(2.5)^2=2(0.083)θ
37.6=θ

The answer I got doesn't match any of the possible answers on my worksheet so I know I'm doing something totally wrong. Please help me out this seemed pretty simple but I got stuck.
 
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What fraction of a circle is 2.5 radians?
 
DTK said:

Homework Statement


A wheel spins at an angular speed of 2.50 rad/s for a total of 30.0s. How many complete revolutions will the wheel make during this time?
A) 31.4 rev
B) 19.3 rev
C) 11.9 rev
D) 75.0 rev

Homework Equations


W=Wo+(alpha)(t)
θ=θo+Wot+1/2(alpha)t^2
W^2=Wo^2+2(alpha)(θ-θo)

The Attempt at a Solution


W=Wo+(alpha)t
2.5rad/s=(alpha)(30s)
Alpha=0.083

W^2=Wo^2+2(alpha)(θ-θo)
(2.5)^2=2(0.083)θ
37.6=θ

The answer I got doesn't match any of the possible answers on my worksheet so I know I'm doing something totally wrong. Please help me out this seemed pretty simple but I got stuck.
There is nothing said about acceleration.

The wheel is rotating at a constant angular (rotational) speed.
 
DTK said:
How many complete revolutions will the wheel make during this time?
 
Chestermiller said:
What fraction of a circle is 2.5 radians?
I have no idea.
 
DTK said:
I have no idea.
How many degrees is 2.5 radians?
 
Chestermiller said:
How many degrees is 2.5 radians?
I got 37.6=θ is that what you are asking?
 
DTK said:
I got 37.6=θ is that what you are asking?
2.5 radians is much more than that.
 
Chestermiller said:
2.5 radians is much more than that.
Okay how do you work it out? I obviously did it wrong. How do I get the right answer to the question
 
  • #10
DTK said:
Okay how do you work it out? I obviously did it wrong. How do I get the right answer to the question
Do you know how to convert radians to degrees or to revolutions?
 
  • #11
Chestermiller said:
Do you know how to convert radians to degrees or to revolutions?
No
 
  • #12
DTK said:
No
Then you are not going to be able to do this problem until you do know. So go look it up in your math book or google radian.
 
  • #13
Chestermiller said:
Then you are not going to be able to do this problem until you do know. So go look it up in your math book or google radian.
2.5 radian equals 143.239 degree according to google
 
  • #14
DTK said:
2.5 radian equals 143.239 degree according to google
How many degrees are the in one revolution?
 
  • #15
Chestermiller said:
How many degrees are the in one revolution?
1 revoltuon equals 360 degrees. 1 degree equals 0.00277 revolutions
 
  • #16
DTK said:
1 revoltuon equals 360 degrees. 1 degree equals 0.00277 revolutions
Excellent. So, based on this, how many revolutions is 143.239 degrees?
 
  • #17
Chestermiller said:
Excellent. So, based on this, how many revolutions is 143.239 degrees?
0.3978
 
  • #18
DTK said:
0.3978
Excellent again. So it's rotating 0.3978 revolutions every second . How many revolutions does it rotate in 30 sec
 
  • #19
Chestermiller said:
Excellent again. So it's rotating 0.3978 revolutions every second . How many revolutions does it rotate in 30 sec
11.9 thank you
 

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