Linear Velocity and Angle
Online calculator and formulas for calculating linear velocity from an angle
Linear Velocity Calculator
Circular motion and linear velocity
Calculates the relationship between linear velocity (v), angle (Δφ), radius (r) and time (t) in circular motions.
Example Calculation
Example: Ferris wheel ride
Problem:
A ferris wheel with a radius of 30 m rotates such that it covers 90° (π/2 radians) in 2 minutes. What is the linear velocity of the passengers?
Given:
- Radius r = 30 m
- Angle Δφ = 90° = π/2 ≈ 1.57 rad
- Time t = 2 min = 120 s
- Find: Linear velocity v
Solution:
1. Calculate arc length:
2. Calculate linear velocity:
Practical applications
Angle and arc length
Important: In circular motions, the arc length Δs = r × Δφ, where Δφ must be given in radians. 360° = 2π rad, so 1° = π/180 rad.
Formulas for linear velocity
Linear velocity describes the speed of a point on a circular path. It depends on the radius, the traversed angle and the required time.
Linear velocity from arc length
Basic formula for linear velocity with known arc length.
Δφ = Angle [rad]
Full circle linear velocity
Linear velocity for a complete revolution (2π rad).
Angular velocity
Relationship between linear and angular velocity.
Angle conversion
Conversion between degrees and radians.
Important notes
- Linear velocity is directed tangentially to the circular path
- In uniform circular motion, linear velocity is constant
- Angles must be entered in radians
- 1 revolution = 360° = 2π rad ≈ 6.28 rad
Detailed description of linear velocity
Physical Fundamentals
Linear velocity describes how fast a point moves on a circular path. It is the velocity along the circular path and always stands tangential to the circle. Linear velocity depends on the radius of the circular path and the angular velocity.
In uniform circular motion, linear velocity is constant, although the direction of velocity constantly changes.
Usage Instructions
Select with the radio buttons which quantity should be calculated. Enter the known values and click "Calculate".
Application Areas
Mechanical Engineering
Gears, pulleys, gear wheels, turbines. Calculation of gear ratios and power transmission.
Automotive Engineering
Wheel speed, speedometer calibration, ESP systems. Foundation for speed measurements and controls.
Astronomy
Planetary orbits, satellite movements, rotational speeds. Calculation of orbital and rotational parameters.
Understanding circular motion
Circular motions can be found everywhere in technology and nature. Important parameters and their relationships:
Linear velocity
v = Δs/t
Velocity along the circular path
Tangential to the circle
Angular velocity
ω = v/r = Δφ/t
Change of angle per time
Unit: rad/s
Centripetal force
F = mv²/r
Force toward the center
Keeps object on circular path
Example: For a car tire with 30 cm radius and 60 km/h driving speed, the wheel rotation speed is about 885 RPM.
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