What is the diameter of the bicycle tire?

Click For Summary

Homework Help Overview

The discussion revolves around determining the diameter of a bicycle tire based on its angular speed and linear speed. The original poster presents the problem using the relationships between angular velocity and linear velocity, specifically referencing the equations for angular speed and linear speed.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the relationship between angular speed and linear speed, with the original poster attempting to solve for the radius and subsequently the diameter. Questions arise regarding the calculations and methods used, particularly focusing on how to manipulate the equations correctly.

Discussion Status

There is an ongoing exploration of the calculations involved in finding the radius and diameter. Some participants provide feedback on the original poster's approach, suggesting corrections and clarifications, while others confirm the results derived from the calculations.

Contextual Notes

The original poster expresses confusion over the calculations and the process of solving for the radius, indicating a need for clarity in handling the equations. There is a mention of the context being a long day at work, which may imply external factors affecting the poster's focus.

keithcuda
Messages
43
Reaction score
0

Homework Statement


A bicycle tire rotates at 30 radians/s. If the bicyclist travels at 10 m/s, what is the diameter of the tire?

Homework Equations


I found; for angular speed, w=v/r
and for linear speed; v=rw
where v=m/s
and w=radians/s

So if i am thinking correctly, i already know my angular speed of 30 radians/s
and my linear speed is 10m/s
so now i just need to find the radius or diameter of the tire.

If i try solving for r, i get completely different answers.

The Attempt at a Solution


bike tire.jpg
 
Physics news on Phys.org
How did you get the 300 in your first solution? Remember what you're solving for, and that you have to treat both sides of an equation the same way.
 
Bystander said:
How did you get the 300 in your first solution? Remember what you're solving for, and that you have to treat both sides of an equation the same way.
good question... It's been a long day here at the power plant.

I always tend to get confused when i try to solve for certain things. i was wanting to solve for "r" by multiplying both sides by 10.

so now i am getting; 30rad/s = 10m/s / r
r=10/30
r=.33

so that is just a radius. The diameter would be .66 meters? or 66cm...?
 
You got that for the second solution, and now for the first solution. That's what I get. And, that should be the diameter.
 
  • Like
Likes   Reactions: keithcuda
Bystander said:
You got that for the second solution, and now for the first solution. That's what I get. And, that should be the diameter.
It makes much more sense when I solve for "r" the proper way... :wThanks for the help
Cheers
Keith
 
Have a happy.
 

Similar threads

Calculating tangential acceleration of rotating object
  • · Replies 2 ·
Replies
2
Views
3K
Relationship Between Bicycle Tire Pressure and Speed
  • · Replies 3 ·
Replies
3
Views
2K
Uniform Circular Motion Bicycle Tire
  • · Replies 1 ·
Replies
1
Views
3K
Angular acceleration of a tire....not sure how to find radius
  • · Replies 3 ·
Replies
3
Views
5K
MHB Determining Miles Traveled From Tire Diameter and Rotations.
  • · Replies 6 ·
Replies
6
Views
2K
Frame of reference of bicycle rider
  • · Replies 2 ·
Replies
2
Views
1K
Angular Acceleration of Bicycle Wheels
  • · Replies 2 ·
Replies
2
Views
6K
Relating Linear and Angular Kinematics
  • · Replies 3 ·
Replies
3
Views
2K
Turning wheel, simply angular momentum
  • · Replies 5 ·
Replies
5
Views
7K
Magnitude of Acceleration on Merry-Go-Round
  • · Replies 2 ·
Replies
2
Views
2K