Calculating Revolutions for a Spinning Wheel | Circular Motion Problem

Click For Summary
SUMMARY

The problem involves calculating the number of complete revolutions made by a wheel spinning at an angular speed of 2.50 rad/s over a duration of 30.0 seconds. The correct calculation shows that the wheel completes 11.9 revolutions during this time. The solution requires converting radians to revolutions, with 2.5 radians equating to approximately 0.3978 revolutions per second. Thus, multiplying this by the total time gives the final answer of 11.9 revolutions.

PREREQUISITES
  • Understanding of angular speed and its units (radians per second)
  • Knowledge of the relationship between radians and revolutions
  • Ability to perform basic unit conversions (radians to degrees, degrees to revolutions)
  • Familiarity with kinematic equations for rotational motion
NEXT STEPS
  • Learn how to convert radians to degrees and revolutions
  • Study the kinematic equations for rotational motion in detail
  • Practice problems involving angular speed and rotational dynamics
  • Explore the concept of angular acceleration and its impact on rotational motion
USEFUL FOR

Students studying physics, particularly those focusing on rotational motion, as well as educators looking for examples of angular speed calculations.

DTK
Messages
9
Reaction score
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.
 
Physics news on Phys.org
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
 

Similar threads

Circular Motion With Constant Angular Acceleration
  • · Replies 3 ·
Replies
3
Views
2K
How to calculate angular speed?
  • · Replies 7 ·
Replies
7
Views
3K
Which Equation Determines Angular Displacement for a Rotating Pulley Wheel?
  • · Replies 1 ·
Replies
1
Views
2K
Why would we ignore initial angular velocity in equation?
  • · Replies 1 ·
Replies
1
Views
8K
Calculating Flywheel Rotations in Angular Speed and Constant Acceleration
  • · Replies 10 ·
Replies
10
Views
2K
Circular Motion - Hanging object swinging around
  • · Replies 7 ·
Replies
7
Views
5K
Archived Simple roulette in terms of circular motion
  • · Replies 2 ·
Replies
2
Views
4K
Circular Motion and Energy Calculations
  • · Replies 11 ·
Replies
11
Views
7K
Finding the tension of the string (vertical circular motion)
  • · Replies 5 ·
Replies
5
Views
3K
A wheel with rotational inertia I = 1/2MR^2
  • · Replies 6 ·
Replies
6
Views
6K