Skip to Content Skip to Header Navigation
Getting your Trinity Audio player ready...

Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.

Case Studies - Circular Motion - help6

For objects moving in circles, the acceleration can be calculated as v2/R where v is the speed and R is the radius of the circle.

There are three similar versions of this question. Here is one of those versions:
 

Version 1:

The speed in Case A is three times that of Case B. The radius is the same in each case. How does the acceleration in Case A compare to the acceleration in Case B?

What This Question Isn't About

Physics is a course that can be filled with formulas. And one way that students often use those formulas is as a recipe to solve problems. They are given numerical values for some of the variables in the equation. They plug those values into the equation. Maybe they do some algebraic manipulation of the equation. And finally they solve for the unknown value. That's not what's going on in this question. Put your calculator and your plug-and-chug mentality away because they won't do you much good on this question.

 

What This Question Is About

In this question, you will need to use the a = v2/R equation. But you need to use it as a guide to thinking about how differing v and R values would affect the acceleration of an object. In this question, you will have to think proportionally. That's quite different than plug-and-chug thinking.

 

Here's How to Think About It:

So one way to think about the equation a = v2/R is to recognize that the acceleration is directly proportional to the square of the speed. So three times the speed results in a 9-fold (32) increase in acceleration. And a one-thirding of the speed results in one-ninth (1/9-th) the acceleration value. So consider the provided information about speed and think about the squared factor that must be used in order to answer the question.

Try these links to The Physics Classroom Tutorial for more help with the mathematics of acceleration for objects moving in a circle.

Acceleration