When describing the way things go in circles, you don’t just use radians; you also can specify the time it takes. The time it takes for an object to complete an orbit is referred to as the *period* of its motion. Period is generally measured in seconds, but it can be measured using other units of time, including milliseconds, minutes, and years.

If an object is traveling at speed *v**,* then the time it takes to go around the circle — the distance it travels in the circle’s circumference, 2π* **r* — will be

Note the symbol of the radius of a circle: *r*. That’s half the circle’s diameter, which is *d*. So *r* = *d*/2. Note also the symbol for the period: *T*. With this equation, given an orbiting object’s speed and the radius of the circle, you can calculate the object’s period.

Another measurement you’ll see in physics problems is *frequency.* Whereas the period is the time an object takes to go around in a circle, the frequency is the number of circles the object makes per unit of time. The frequency, *f**,* is connected to the period like this:

Frequency is most often measured in units of cycles per second (cps), which are also called Hertz (Hz). An object moving in a circle with a frequency of 2.0 Hz completes two trips around its circle every second.

## Sample question

The moon’s orbital radius is 3.85 x 10

^{8}m, and its period is about 27.3 days. What is its speed as it goes around Earth?The correct answer is 1,020 m/s, when rounded for significant figures.

Convert 27.3 days to seconds:

Use the equation for the period to solve for speed:

Plug in the numbers:

## Practice questions

You have a ball on a string, and you’re whipping it around in a circle. If the radius of its circle is 1.0 m and its period is 1.0 s, what is its speed?

You have a toy plane on a wire, and it’s traveling around in a circle. If the radius of its circle is 10.0 m and its period is 0.75 s, what is its speed?

Following are answers to the practice questions:

6.3 m/s

Use the equation for the period to solve for speed:

Plug in the numbers:

84 m/s

Use the equation for the period to solve for speed:

Plug in the numbers: