Calculating Revolutions for a Spinning Wheel | Circular Motion Problem

AI Thread Summary
A wheel spinning at an angular speed of 2.50 rad/s for 30 seconds will complete 11.9 revolutions. The calculations involved converting radians to degrees and then to revolutions, with 2.5 radians equating to approximately 143.239 degrees. The conversion showed that 1 revolution equals 360 degrees, leading to the conclusion that 143.239 degrees corresponds to about 0.3978 revolutions per second. Multiplying this by the total time of 30 seconds results in 11.9 revolutions. The problem emphasizes the importance of understanding unit conversions in circular motion calculations.
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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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