Chapter 10, Problem 44A

As a car speeds up when rounding a curve, does centripetal acceleration also increase? Use an equation to defend your answer.

To determine

Whether the centripetal acceleration also increases when a car speeds up when rounding a curve.

Answer to Problem 44A

Yes

Explanation of Solution

Introduction:

When an object moves around a circle of radius $r$ with a tangential speed $v$ , then the centripetal acceleration is given by,

  $a_c=\frac{v^2}{r}$

Using the above formula, if the radius is constant, then

  $a_c\propto v^2$

Now, when a car speeds up when rounding a curve, then because of the radius of the curve being constant, the centripetal acceleration increases with the increase in the speed.

Conclusion:

Hence, the increase in the speed of the car along the curve results in the increase of the centripetal acceleration.