Linear Velocity in Circular Motion Calculator

Calculator Inputs

Choose a solve mode, enter known values, and keep the unused fields blank.

Solve for

Motion input basis

Decimal places

Radius

Linear velocity

Angular velocity

RPM

Frequency

Hz

Period

s

Observation time

Graph max radius

Graph points

Example Data Table

Radius (m)	RPM	Angular Velocity (rad/s)	Linear Velocity (m/s)	Period (s)
0.25	60	6.2832	1.5708	1.0000
0.50	120	12.5664	6.2832	0.5000
1.00	90	9.4248	9.4248	0.6667
1.50	45	4.7124	7.0686	1.3333

Formula Used

Linear velocity: v = r × ω
Using frequency: v = 2πr f
Using period: v = 2πr / T
Using RPM: ω = 2π × RPM / 60
Angular velocity: ω = v / r
Radius: r = v / ω
Frequency: f = ω / 2π
Period: T = 1 / f
Centripetal acceleration: a_c = v² / r
Circumference: C = 2πr

How to Use This Calculator

Select the quantity you want to solve for.
Choose the motion input basis when required.
Enter the known values and select matching units.
Add an observation time to estimate distance and revolutions.
Set graph radius and point count if needed.
Press Calculate Now to show the result above the form.
Use the download buttons for CSV and PDF exports.

Frequently Asked Questions

1) What is linear velocity in circular motion?

Linear velocity is the tangential speed of an object moving around a circle. It describes how fast the object travels along the circular path at a specific radius.

2) How is linear velocity different from angular velocity?

Linear velocity measures path speed in distance per time. Angular velocity measures turning rate in angle per time. They are linked by v = r × ω.

3) Why does a larger radius increase linear velocity?

At the same angular velocity, a larger radius means the object covers a longer path each revolution. That longer path raises tangential speed.

4) Can I use RPM instead of angular velocity?

Yes. RPM is a practical rotational input. The calculator converts RPM into angular velocity internally, then uses the circular motion formulas automatically.

5) What unit should I use for radius?

Use any supported length unit that matches your data source. The calculator converts everything internally, so meters, feet, centimeters, millimeters, and inches all work.

6) What does the period tell me?

The period is the time needed for one full revolution. A smaller period means faster rotation and usually a higher linear velocity at the same radius.

7) What is centripetal acceleration used for?

Centripetal acceleration shows how strongly motion bends toward the center. It is useful in machinery, vehicle cornering, rotating tools, and orbit analysis.

8) Why is the graph helpful?

The graph shows how tangential speed changes with radius for the current angular velocity. It makes scaling behavior easy to compare across different design cases.