What is the diameter of the bicycle tire?

In summary, the bicycle tire has an angular speed of 30 radians/s and a linear speed of 10 m/s. To find the diameter of the tire, we can use the equations w=v/r and v=rw, where w is in radians/s and v is in m/s. Solving for r, we get a radius of 0.33 meters, which means the diameter of the tire is 0.66 meters or 66 cm.
  • #1
keithcuda
43
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
 
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  • #2
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.
 
  • #3
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...?
 
  • #4
You got that for the second solution, and now for the first solution. That's what I get. And, that should be the diameter.
 
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Likes keithcuda
  • #5
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
 
  • #6
Have a happy.
 

Related to What is the diameter of the bicycle tire?

1. What is the standard diameter of a bicycle tire?

The standard diameter of a bicycle tire is 26 inches for mountain bikes, 27 inches for road bikes, and 28 inches for hybrid bikes. However, there are also other sizes available, such as 24 inches for children's bikes and 29 inches for larger mountain bikes.

2. How do I measure the diameter of my bicycle tire?

To measure the diameter of your bicycle tire, place your bike upside down and use a tape measure to measure the distance from the center of the wheel to the outside edge of the tire. You can also find the tire size printed on the sidewall of the tire.

3. Why is the diameter of a bicycle tire important?

The diameter of a bicycle tire is important because it affects the overall size and performance of the bike. A larger tire diameter can provide more stability and speed, while a smaller diameter may be more suitable for maneuverability and agility.

4. Can I change the diameter of my bicycle tire?

Yes, you can change the diameter of your bicycle tire by purchasing a different size tire that is compatible with your bike's wheel size. However, it is important to make sure that the new tire will fit properly and not cause any issues with the bike's performance.

5. How often should I replace my bicycle tire due to wear and tear?

It is recommended to replace your bicycle tire every 1,000-2,000 miles or every 2-3 years, depending on usage and road conditions. It is important to regularly check the tire tread and replace the tire if there are any signs of wear and tear, such as bald spots or cracks.

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