Linear Speed Calculator
Calculate the linear (tangential) speed of a point on a rotating object using our simple linear speed calculator. Enter the radius and rotational speed below.
Linear Speed at Different Radii
| Radius | Linear Speed (m/s) | Linear Speed (km/h) | Linear Speed (mph) |
|---|---|---|---|
| Enter values and calculate to see table. | |||
Linear Speed vs. Radius & RPM
What is a Linear Speed Calculator?
A linear speed calculator is a tool used to determine the speed of a point moving along a circular path. This speed is also known as tangential speed because the direction of motion is tangent to the circle at any given point. It's the straight-line speed the point would have if it were suddenly released from its circular path. This linear speed calculator takes the radius of the circular path and the rotational speed (often given in Revolutions Per Minute, or RPM) as inputs to find the linear speed.
Anyone studying or working with rotating objects might use a linear speed calculator. This includes engineers designing machinery, physicists studying rotational motion, students doing homework, or even someone curious about the speed of a point on a spinning wheel or a car tire. The linear speed calculator helps convert rotational motion parameters into linear motion parameters.
A common misconception is that all points on a rigid rotating object have the same linear speed. While all points have the same angular speed (how fast they rotate), their linear speeds depend on their distance from the axis of rotation (the radius). Points further from the center move faster linearly.
Linear Speed Formula and Mathematical Explanation
The linear speed (v) of a point on a rotating object is directly proportional to its distance from the center of rotation (radius, r) and the angular velocity (ω) of the object.
The formula is:
v = r × ω
Where:
- v is the linear speed.
- r is the radius (distance from the center of rotation).
- ω is the angular velocity.
Angular velocity (ω) is often derived from the rotational speed given in Revolutions Per Minute (RPM). To convert RPM to radians per second (the standard unit for ω):
ω (radians/second) = RPM × (2π radians / 1 revolution) × (1 minute / 60 seconds) = RPM × 2π / 60
So, the full formula using RPM is:
v = r × (RPM × 2π / 60)
It's crucial to ensure the radius 'r' is in consistent units (like meters) with the desired output speed units (like meters per second).
Variables Table
| Variable | Meaning | Unit (SI) | Typical Range |
|---|---|---|---|
| v | Linear Speed (Tangential Speed) | m/s | 0 to very high |
| r | Radius | m | 0 to large values |
| ω | Angular Velocity | rad/s | 0 to high values |
| RPM | Revolutions Per Minute | rev/min | 0 to tens of thousands |
| f | Frequency (Revolutions per second, RPS) | Hz (s-1) | RPM/60 |
| π | Pi | – | ~3.14159 |
Practical Examples (Real-World Use Cases)
Example 1: Car Tire
A car tire has a radius of 0.35 meters and is rotating at 800 RPM. What is the linear speed of a point on the outer edge of the tire?
Inputs:
- Radius (r) = 0.35 m
- RPM = 800
Calculation:
- ω = 800 * 2π / 60 ≈ 83.78 rad/s
- v = 0.35 m * 83.78 rad/s ≈ 29.32 m/s
The linear speed of the edge of the tire relative to the axle is about 29.32 m/s (or about 105.5 km/h or 65.6 mph). This linear speed calculator can quickly give you this result.
Example 2: Hard Drive Platter
A hard drive platter spins at 7200 RPM. A data track is located at a radius of 4 cm (0.04 m) from the spindle.
Inputs:
- Radius (r) = 0.04 m
- RPM = 7200
Calculation:
- ω = 7200 * 2π / 60 ≈ 753.98 rad/s
- v = 0.04 m * 753.98 rad/s ≈ 30.16 m/s
The linear speed of the data track is about 30.16 m/s. Using a linear speed calculator helps engineers understand data read/write speeds.
How to Use This Linear Speed Calculator
- Enter Radius: Input the distance from the center of rotation to the point of interest in the "Radius (r)" field.
- Select Radius Unit: Choose the appropriate unit for the radius (meters, centimeters, inches, etc.) from the dropdown menu. The linear speed calculator will convert it to meters for calculation.
- Enter Rotational Speed: Input the speed in Revolutions Per Minute (RPM) into the "Rotational Speed (RPM)" field.
- Calculate: Click the "Calculate Speed" button, or see the results update automatically if you changed input values.
- Read Results: The primary result is the linear speed displayed prominently. You'll also see intermediate values like angular velocity in rad/s, RPS, and the radius in meters. The linear speed calculator provides these for better understanding.
- Table and Chart: Observe the table and chart below the main calculator to see how linear speed changes with different radii at the given RPM, and how it varies with RPM and radius graphically.
- Reset: Click "Reset" to return to default values.
- Copy: Click "Copy Results" to copy the main speed, intermediate values, and input parameters.
This find linear speed calculator is designed for ease of use while providing comprehensive results.
Key Factors That Affect Linear Speed Results
- Radius (r): The most direct factor. Linear speed is directly proportional to the radius. Doubling the radius doubles the linear speed, assuming angular velocity remains constant.
- Angular Velocity (ω) or RPM: Linear speed is also directly proportional to the angular velocity (or RPM). Doubling the RPM doubles the linear speed for a given radius.
- Units of Radius: The units used for the radius input significantly affect the calculation if not converted correctly. Our linear speed calculator handles common unit conversions.
- Rotational Frequency (f): This is the number of revolutions per second (RPS), equal to RPM/60. It's directly related to angular velocity (ω = 2πf).
- Point of Interest: The specific point on the rotating object whose linear speed you want to find determines the radius 'r'.
- Rigidity of the Object: The formulas used by the linear speed calculator assume a rigid body, where all points rotate with the same angular velocity. For non-rigid bodies, the situation is more complex.