Learning Goal:

To be able to identify key characteristics about the velocity and acceleration of a body that is experiencing motion in a cylindrical coordinate system.

Three stock car drivers are racing around a circular bend. They are each circling the bend at different radii: r1=229 m , r2=235 m , and r3=241 m . At a given instant, all three are traveling at the same transverse rate of rotation, θ˙1=θ˙2=θ˙3=0.285 rad/s .The cars are also increasing their transverse rate of rotation by the same rate, θ¨1=θ¨2=θ¨3=2.85×10−2 rad/s2 .

(Figure 1)

 

 

 

 

 

Determining the magnitudes of the velocity and acceleration of the first driver

Determine the magnitudes of the velocity and acceleration of the first driver.

Express your two answers, separated by a comma, to two significant figures in meters per second and meters per second squared.

v1, a1=

65,20

m/s, m/s2

Determining the magnitudes of the velocity and acceleration of the second driver

Determine the magnitudes of the velocity and acceleration of the second driver.

Express your two answers, separated by a comma, to two significant figures in meters per second and meters per second squared.

v2, a2=

67,20

m/s, m/s2

 

Finding the equation for the overall magnitude of velocity and acceleration

Identify the equations for the overall magnitude of the velocity and acceleration of the driver in terms of the radius of curvature, r, the transverse rate of rotation, θ˙, and the transverse rate of acceleration, θ¨. 

v=rθ˙, a=(−rθ˙2)2+(rθ¨)2−−−−−−−−−−−−√