Uniform circular motion is motion around a circle at constant speed. This page focuses on timing one full revolution and connecting that timing to frequency and speed using simple, algebra-based relationships.

Core ideas: “one full revolution”

In uniform circular motion, an object travels around a circular path while its speed (magnitude of velocity) stays constant.

A labeled circular-motion diagram showing tangential velocity vectors at multiple points on the path, with the radius $r$ drawn from the center to the object. The figure helps distinguish the circular path from the instantaneous direction of motion (tangent), clarifying what “speed along the circular path” means. Source

A revolution means one complete trip around the circle, returning to the same position on the path.

The distance travelled in one full revolution is the circle’s circumference, $2\pi r$, where $r$ is the radius. Time-based quantities (period and frequency) describe how quickly those revolutions happen.

Period

Key points:

• Units: seconds (s)

• “Longer period” means each revolution takes more time, so the motion cycles more slowly.

• In lab situations, $T$ is often found by timing multiple revolutions and dividing by the number of revolutions to reduce reaction-time error.

Frequency

Frequency describes “how many per second” rather than “how long for one.” It is commonly reported in hertz (Hz), where $1\ \text{Hz} = 1\ \text{s}^{-1}$.

Relationship between period and frequency

Period and frequency are reciprocals: if an object completes more revolutions each second, the time for one revolution must be smaller.

A time-domain graph showing repeated cycles, making the period $T$ identifiable as the horizontal length of one repeat. Since frequency counts cycles per second, the figure supports the reciprocal relationship $f=\frac{1}{T}$ as a direct reading from the cycle spacing on the time axis. Source

This relationship is only about counting cycles and time; it does not depend on the radius or the object’s mass.

Connecting period/frequency to speed in uniform circular motion

For uniform circular motion, “speed” means the constant rate of distance travelled along the circular path. In one revolution, the object travels $2\pi r$ in a time $T$.

A labeled uniform-circular-motion diagram showing that one complete lap covers the circumference $2\pi r$ and takes one period $T$. It emphasizes that speed along the path is distance-per-time for one revolution, giving $v=\frac{2\pi r}{T}$. Source

You can also express the same idea using frequency, since $T=1/f$. This is useful if frequency is measured directly (for example, from a rotation sensor).

Interpreting changes

• If radius increases while $T$ stays the same, then speed increases (more distance per revolution in the same time).

• If frequency increases while $r$ stays the same, then speed increases (more revolutions each second means more circumference covered each second).

• If period doubles, the speed is cut in half (same circumference, more time per revolution).

Common unit conversions (rotation contexts)

You may see rotational rates in revolutions per minute (rpm). Converting to Hz aligns with $f$ in the equations:

• Divide by 60: $\text{Hz} = \text{rpm}/60$

• Multiply by 60: $\text{rpm} = 60\cdot \text{Hz}$