Case Studies - Circular Motion - help2

The speed of an object can always be calculated as a distance traveled per time of travel. For objects moving in circles, this is often the circumference per period. The circumference is the distance for one pass around the circle and the period is the time for one pass around the circle. Thus the speed is 2•π•R/T where R is the radius of the circle and T is the period.

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 equation v = 2•π•R/T to answer the question. But you need to use it as a guide to thinking about how differing R and T values would affect the speed 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 v = 2•π•R/T is to recognize that the speed is inversely proportional to the period. So a doubling or tripling of the period without a change in the radius will result in a halving or a one-thirding of the speed. If an object travels around a circle with twice the period but no change in circumference (same radius), then that object is covering the same distance in twice the time. This means the object will have one-half the speed.