Circular Motion

Calculator and formulas for calculating circular motion

Circular Motion Calculator

Uniform circular motion

Calculates the relationship between linear velocity (v), radius (r), period (T) and frequency (f) in constant circular motion.

Result
Linear velocity:
Radius:
Period:
Frequency:

Example Calculation

Example: Ferris wheel
Problem:

A ferris wheel with a 30 m radius takes 4 minutes for one complete revolution. What is the linear velocity of the passengers?

Given:
  • Radius r = 30 m
  • Period T = 4 min = 240 s
  • Find: Linear velocity v
Solution:

1. Calculate circumference:

\[U = 2\pi r = 2\pi \times 30 = 188.5 \text{ m}\]

2. Calculate linear velocity:

\[v = \frac{U}{T} = \frac{2\pi r}{T}\]
\[v = \frac{188.5 \text{ m}}{240 \text{ s}} = 0.79 \text{ m/s}\]
\[v = 0.79 \times 3.6 = 2.8 \text{ km/h}\]
Practical applications
Mechanical engineering: Gears, pulleys, transmissions
Amusement parks: Ferris wheels, carousels, rides
Automotive engineering: Wheel speed, cornering, engine control
Understanding circular motion

Uniform circular motion: The linear velocity is constant, but the direction changes continuously. This creates a centripetal acceleration toward the center of the circle.

Formulas for circular motion

Uniform circular motion is a fundamental form of motion in physics. With constant linear velocity, only the direction of motion changes continuously.

Linear velocity

Velocity along the circular path, calculated from circumference and period.

\[v = \frac{U}{T} = \frac{2\pi r}{T}\]
v = Linear velocity [m/s]
U = Circumference [m]
r = Radius [m]
T = Period [s]
Calculate radius

Radius from linear velocity and period.

\[r = \frac{vT}{2\pi}\]
Rearrangement of the basic formula for radius.
Period

Time for one complete revolution.

\[T = \frac{2\pi r}{v}\]
Period of circular motion from radius and velocity.
Frequency

Number of revolutions per unit time.

\[f = \frac{1}{T} = \frac{v}{2\pi r}\]
f = Frequency [Hz] or [rev/s]
Additional relationships
Angular velocity:
ω = 2π/T = 2πf
ω = v/r
Centripetal acceleration:
a = v²/r = ω²r
a = 4π²r/T²
Units:
Frequency: RPM, Hz
ω: rad/s

Detailed description of circular motion

Physical Fundamentals

Uniform circular motion occurs when a body moves with constant linear velocity on a circular path. Although the speed is constant, the direction changes continuously, resulting in centripetal acceleration.

This form of motion is fundamental for understanding rotating systems in engineering and nature.

Usage Instructions

Select with the radio buttons which quantity should be calculated. The calculator automatically computes the frequency as well.

Application Areas

Mechanical Engineering

Transmissions, pulleys, gears, turbines. Design of drive systems and gear ratios.

Amusement Industry

Ferris wheels, carousels, roller coasters. Safety calculations and comfort assessment.

Automotive Engineering

Wheel speed, cornering, engine control. ABS systems and vehicle dynamics control.

Circular motion in practice

Circular motions occur daily in various forms. Here are typical examples and their characteristic values:

Everyday devices

CD player: ~500 RPM
Washing machine: ~1400 RPM
Blender: ~15000 RPM

Vehicles

Car tire: ~800 RPM
Motorcycle: ~6000 RPM
Jet turbine: ~10000 RPM

Amusement parks

Ferris wheel: ~0.5 RPM
Carousel: ~6 RPM
Centrifuge: ~30 RPM

Tip: At high rotational speeds, centrifugal force becomes very large. Therefore, rotating parts must be constructed particularly robustly!


More physics functions

Centrifugal Force • Efficiency • Inclined plan • kW - hp converter • PS - hp converter • Power Force Displacement and Time • Pressure, Force and Area • Torque • Weight Force • Work, Force and Displacement • Work Power and Time • Energy Density • Kinetic Energy • Specific Energy • Acceleration by Distance • Acceleration by Time • Angular Velocity • Circular Motion • Rotational Speed • Speed, Distance and Time • Free-Fall • Temperature in Atmosphere • Mach Number • Speed of sound • Sound Pressure • Belt Length • Gear Ratio • Angle of refraction