Asked by kyle
A race car, starting from rest, travels around a circular turn of radius 29.3 m. At a certain instant, the car is still accelerating, and its angular speed is 0.621 rad/s. At this time, the total acceleration (centripetal plus tangential) makes an angle of 35.0° with respect to the radius. (The situation is similar to that in Figure 8.15b.) What is the magnitude of the total acceleration?
Answers
Answered by
drwls
The centripetal part of the acceleration is
a,c = r w^2 = (29.3)*(0.621)^2 = 11.32 m/s^2
It is directed toward the center of the circle. The tangential acceleration a,t is such that
a,t/a,c = tan 35 = 0.700
The tangential acceleration is therefore
a,t = 16.17 m/s^2
The total acceeration a is such that
(a,c)/ a = sin 35
a = 19.74 m/s^2
a,c = r w^2 = (29.3)*(0.621)^2 = 11.32 m/s^2
It is directed toward the center of the circle. The tangential acceleration a,t is such that
a,t/a,c = tan 35 = 0.700
The tangential acceleration is therefore
a,t = 16.17 m/s^2
The total acceeration a is such that
(a,c)/ a = sin 35
a = 19.74 m/s^2
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