Circular Motion Calculator
Calculate all parameters of uniform circular motion including period, frequency, angular velocity, and centripetal acceleration
Calculate Circular Motion Parameters
Time for one complete revolution
Required for linear velocity and acceleration calculations
Circular Motion Results
Key Formulas:
• f = 1/T | ω = 2πf = 2π/T
• v = ωr | ac = v²/r = ω²r
• Circumference = 2πr
• Angular displacement (1s) = ω × 1s = 0.000 rad
Motion Analysis
Example Calculation
Ferris Wheel Example
Given: A Ferris wheel with radius 15m makes one complete revolution in 30 seconds
Find: All circular motion parameters
Solution:
• Period (T) = 30 s (given)
• Frequency (f) = 1/T = 1/30 = 0.033 Hz
• Angular velocity (ω) = 2π/T = 2π/30 = 0.209 rad/s
• Linear velocity (v) = ωr = 0.209 × 15 = 3.14 m/s
• Centripetal acceleration (ac) = v²/r = (3.14)²/15 = 0.66 m/s²
Earth's Rotation Example
Given: Earth completes one rotation in 24 hours
Find: Angular velocity and linear velocity at equator (radius ≈ 6,371 km)
Solution:
• Period (T) = 24 × 3600 = 86,400 s
• Angular velocity (ω) = 2π/86,400 = 7.27 × 10⁻⁵ rad/s
• Linear velocity at equator = ω × r = 7.27 × 10⁻⁵ × 6,371,000 = 463 m/s
Types of Circular Motion
Uniform Circular Motion
Constant speed along circular path
Velocity direction changes, magnitude constant
Non-uniform Circular Motion
Variable speed along circular path
Both speed and direction change
Key Relationships
Period and Frequency
f = 1/T
Angular Velocity
ω = 2πf = 2π/T
Linear Velocity
v = ωr
Centripetal Acceleration
ac = v²/r = ω²r
Physics Tips
Centripetal force always points toward the center
Velocity is always tangent to the circular path
Angular velocity is the same for all points on a rigid body
Linear velocity increases with distance from center
Understanding Circular Motion
What is Circular Motion?
Circular motion occurs when an object moves along a circular path. The motion can be uniform (constant speed) or non-uniform (variable speed). Key characteristics include continuous change in direction and the requirement of centripetal force toward the center.
Key Parameters
- •Period (T): Time for one complete revolution
- •Frequency (f): Number of revolutions per unit time
- •Angular velocity (ω): Rate of change of angular position
- •Centripetal acceleration: Acceleration toward the center
Mathematical Relationships
Basic Relationships:
f = 1/T
ω = 2πf = 2π/T
v = ωr
ac = v²/r = ω²r = 4π²r/T²
Real-World Examples
- • Earth's rotation and revolution
- • Ferris wheels and carousels
- • Planetary motion
- • Centrifuges in laboratories
- • Car wheels and bicycle wheels
- • Washing machine spin cycles