# Angular Speed of Tires

1. Mar 30, 2012

### eagles12

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

w=θ/t

3. The attempt at a solution

θ=d/r
θ=d/31

2. Mar 30, 2012

### Staff: Mentor

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.

3. Mar 30, 2012

### eagles12

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

4. Mar 30, 2012

### 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.

5. Mar 30, 2012

### eagles12

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

6. Mar 30, 2012

### Sefrez

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

7. Mar 30, 2012

### eagles12

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

8. Mar 30, 2012

### Sefrez

Maybe you have over rounded?

9. Mar 30, 2012

### eagles12

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

10. Mar 30, 2012

### Sefrez

Ok. So you have the answer now? :)

11. Mar 30, 2012

### eagles12

its still saying my answer is incorrect

12. Mar 30, 2012

### Sefrez

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

13. Mar 30, 2012

### eagles12

got it! thanks!