Radial and Transverse Acceleration

[aaronfue]

Homework Statement

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.

Homework Equations

a=√a_r²+a_\theta²

a_r=\ddot{r} - r\dot{\theta}²

a_θ=r\ddot{\theta} + 2\dot{r}\dot{\theta}

The Attempt at a Solution

a_r=18.286809 \frac{rad}{s^2}
a_θ=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?

 

[mfb]

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.

 

[aaronfue]

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.

Is this the answer:

v = w*r
= 0.271 rad/s * 249m
= 67.48m/s

 

[mfb]

That is right.

 

[aaronfue]

That is right.

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

Thanks for your help!