Calculating Revolutions for a Spinning Wheel | Circular Motion Problem

In summary, the wheel rotates at an angular speed of 2.50 rad/s for 30.0 s and makes 11.9 complete revolutions during this time. To determine this, we need to convert radians to degrees and then use the fact that one revolution is equal to 360 degrees.
  • #1
DTK
9
0

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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  • #2
What fraction of a circle is 2.5 radians?
 
  • #3
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.
 
  • #4
DTK said:
How many complete revolutions will the wheel make during this time?
 
  • #5
Chestermiller said:
What fraction of a circle is 2.5 radians?
I have no idea.
 
  • #6
DTK said:
I have no idea.
How many degrees is 2.5 radians?
 
  • #7
Chestermiller said:
How many degrees is 2.5 radians?
I got 37.6=θ is that what you are asking?
 
  • #8
DTK said:
I got 37.6=θ is that what you are asking?
2.5 radians is much more than that.
 
  • #9
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
 

FAQ: Calculating Revolutions for a Spinning Wheel | Circular Motion Problem

What is circular motion and why is it important?

Circular motion refers to the movement of an object along a circular path. It is important because many real-world systems, such as spinning wheels, planets orbiting the sun, and amusement park rides, involve circular motion. Understanding circular motion allows scientists to predict and control the behavior of these systems.

How do you calculate the number of revolutions for a spinning wheel?

To calculate the number of revolutions for a spinning wheel, you need to know the angular velocity (ω) and the time (t) it takes for the wheel to complete one revolution. The formula for calculating revolutions is N = ωt / 2π, where N is the number of revolutions.

What is angular velocity and how is it measured?

Angular velocity is the rate at which an object rotates or spins. It is measured in radians per second (rad/s) or revolutions per minute (rpm). Angular velocity can be calculated by dividing the angular displacement (change in angle) by the time it takes for the displacement to occur.

What is the difference between linear and angular velocity?

Linear velocity refers to the speed or rate at which an object moves in a straight line, while angular velocity refers to the speed or rate at which an object rotates or spins. Linear velocity is measured in meters per second (m/s) or kilometers per hour (km/h), while angular velocity is measured in radians per second (rad/s) or revolutions per minute (rpm).

What are some real-world applications of calculating revolutions for a spinning wheel?

Calculating revolutions for a spinning wheel has many practical applications, such as predicting the performance of a car engine, designing gears and pulleys for machinery, and understanding the motion of objects in space. It is also used in sports, such as calculating the rotation of a basketball or the spin rate of a baseball pitch.

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