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

[eagles12]

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

 

[berkeman]

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.

 

[eagles12]

circumference=194.77
12=wr
im not sure if that is the way to use the 12

 

[Sefrez]

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.

 

[eagles12]

so 194.77=the distance traveled
so θ=6.2829
so w=.3871 does this seem right?

 

[Sefrez]

Did you make sure to convert the radius from cm to m?

 

[eagles12]

after i converted i got 39 but it says that is incorrect

 

[Sefrez]

Maybe you have over rounded?

 

[eagles12]

i went to four significant figures in each calculation but i had to give my answer in two

 

[Sefrez]

Ok. So you have the answer now? :)

 

[eagles12]

its still saying my answer is incorrect

 

[Sefrez]

The angular speed should be ~38.71 rad/s as you had before converting cm to m.

 

[eagles12]

got it! thanks!