About

In kinematics, determining how fast a specific point on a rotating object travels depends on two factors: the rate of rotation and the distance from the axis (radius). This distinction is critical in mechanical engineering, where a turbine blade tip experiences significantly higher stress and speed than the hub, despite sharing the same RPM.

This tool bridges the gap between angular frequency and tangential velocity. It standardizes inputs by converting all rotational units (RPM, degrees/second) into radians per second before applying the fundamental radius multiplier. This ensures compliance with SI unit standards and provides accurate velocity data for safety tolerances in centrifuges, wheels, and engines.

Formulas

Linear velocity v is the product of the radius r and the angular velocity ω, provided ω is expressed in radians per second.

v = r × ω

If the input is in Revolutions Per Minute (RPM), a pre-conversion step is required:

ω_rad/s = RPM × 2π60

Reference Data

Object	Angular Speed (ω)	Radius (r)	Linear Velocity (v)
Vinyl Record (LP)	33 RPM	0.146 m	0.51 m/s
Car Wheel (Hwy)	840 RPM	0.3 m	26.4 m/s (95 km/h)
Washing Machine	1200 RPM	0.25 m	31.4 m/s
Hard Drive (HDD)	7200 RPM	0.045 m	33.9 m/s
Helicopter Tip	300 RPM	7.0 m	220.0 m/s
Table Saw Blade	3450 RPM	0.127 m	45.9 m/s
Earth Equator	0.00069 RPM	6371 km	460 m/s
Dental Drill	400k RPM	0.005 m	104.7 m/s

Frequently Asked Questions

Angular velocity measures rotation rate, which is constant for the entire rigid body. Linear velocity measures actual distance traveled per second. A point on the rim must travel a larger circumference than a point near the center in the same amount of time, necessitating a higher speed.

The formula specifically requires radius. If you have the diameter, you must divide it by 2 before inputting. Using diameter directly will yield a result double the actual velocity.

No. This tool uses classical Newtonian mechanics. It is accurate for all terrestrial engineering applications but does not apply to objects approaching the speed of light.

Select the "Degrees/sec" option in the unit dropdown. The tool automatically applies the factor π180 to convert your input to radians before calculating linear velocity.