Example 6.2 from College Physics, 6.2 Centripetal Acceleration

How Does the Centripetal Acceleration of a Car Around a Curve Compare with That Due to Gravity?

What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed. See Figure 6.9(a).

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Because $v$ and $r$ are given, the first expression in $a_{c} = \frac{v^{2}}{r};a_{c} = {rω}^{2}$ is the most convenient to use.
Solution
Entering the given values of $v = 25 . 0 m/s$ and $r = 500 m$ into the first expression for $a_{c}$ gives
$a_{c} = \frac{v^{2}}{r} = \frac{(25.0 m/s)^{2}}{500 m} = 1 . 25 {m/s}^{2} .$
6.18
Discussion
To compare this with the acceleration due to gravity $(g = 9 . 80 {m/s}^{2})$ , we take the ratio of $a_{c} / g = (1.25 {m/s}^{2}) / (9.80 {m/s}^{2}) = 0 . 128$ . Thus, $a_{c} = 0 . 128 g$ and is noticeable especially if you were not wearing a seat belt.

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