1. Jan 30, 2013

### aaronfue

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

Three stock car drivers are racing around a circular bend. They are each circling the bend at different radii: r1=249 m, r2=255 m, and r3=261 m. At a given instant, all three are traveling at the same transverse rate of rotation, $\dot{\theta}$1=$\dot{\theta}$2=$\dot{\theta}$3=0.271 $\frac{rad}{s}$ .The cars are also increasing their transverse rate of rotation by the same rate, $\ddot{\theta}$1=$\ddot{\theta}$2=$\ddot{\theta}$3=2.71×10-2$\frac{rad}{s^2}$.Determine the magnitudes of the velocity and acceleration of the first driver.

2. Relevant equations

a=√ar2+a$\theta$2

ar=$\ddot{r}$ - r$\dot{\theta}$2

aθ=r$\ddot{\theta}$ + 2$\dot{r}$$\dot{\theta}$

3. The attempt at a solution

ar=18.286809 $\frac{rad}{s^2}$
aθ=6.7479 $\frac{rad}{s^2}$
a=√18.2868092 + 6.74792 = 19.492 $\frac{rad}{s^2}$

v = ??

I'm not sure if the velocity is 18.286809 $\frac{rad}{s^2}$ or not?

Last edited: Jan 30, 2013
2. Jan 30, 2013

### Staff: Mentor

I would calculate this in cartesian coordinates.
And rad/s^2 as unit does not make sense for the magnitude of an acceleration.

If you travel in a circle with a radius of 249m with an angular velocity of 0.271 rad/s, what is your velocity? Hint: It is a very easy formula.

3. Jan 30, 2013

### aaronfue

v = w*r
= 67.48m/s

4. Jan 30, 2013

### Staff: Mentor

That is right.

5. Jan 30, 2013

### aaronfue

I see. I didn't find this in my textbook, "Engineering Mechanics: Dynamics" by Hibbeler. I'll have to remember this.