What is the Angular Speed of Tires with a Radius of 31 cm and a Speed of 12 m/s?

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Homework Help Overview

The problem involves calculating the angular speed of car tires with a specified radius of 31 cm when the car is moving at a speed of 12 m/s. The discussion centers around the relationship between linear speed and angular speed, particularly in the context of rolling motion without slipping.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between linear distance traveled and the angular displacement of the tires. There are attempts to relate the given speed to the angular speed using the formula for circumference and angular velocity.

Discussion Status

The discussion is ongoing, with participants exploring different calculations and questioning the accuracy of their results. Some guidance has been offered regarding unit conversion and the importance of maintaining significant figures in calculations.

Contextual Notes

Participants have noted the need to convert the radius from centimeters to meters and have discussed the implications of rounding in their calculations. There is an emphasis on ensuring consistent units throughout the problem.

eagles12
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Homework Statement



The tires of a car have a radius of 31 cm. What is the angular speed of these tires when the car is driven at 12 m/s?

Homework Equations



w=θ/t

The Attempt at a Solution



θ=d/r
θ=d/31
 
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eagles12 said:

Homework Statement



The tires of a car have a radius of 31 cm. What is the angular speed of these tires when the car is driven at 12 m/s?

Homework Equations



w=θ/t

The Attempt at a Solution



θ=d/r
θ=d/31

Maybe you could try to expand a bit on your attempt at the solution? You didn't even include the velocity of 12m/s in your attempt.

What is the circumference of tires that have a radius of 31 cm? Be sure to keep units consistent -- usually you convert it all into meters.
 
circumference=194.77
12=wr
im not sure if that is the way to use the 12
 
The tangental speed of the tires are the same as the speed of the car. This is because there is assumed no slipping of the tires - they are always in "non-moving" contact, just rolling. In other words, the distance the car travels in time t is equal to the distance gone around the circumference of the tires in time t. Think of the tire laying out a "print"/line as its contact point rolls some distance.

Thinking about this should help you solve this problem.
 
so 194.77=the distance traveled
so θ=6.2829
so w=.3871 does this seem right?
 
Did you make sure to convert the radius from cm to m?
 
after i converted i got 39 but it says that is incorrect
 
Maybe you have over rounded?
 
i went to four significant figures in each calculation but i had to give my answer in two
 
  • #10
Ok. So you have the answer now? :)
 
  • #11
its still saying my answer is incorrect
 
  • #12
The angular speed should be ~38.71 rad/s as you had before converting cm to m.
 
  • #13
got it! thanks!
 

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