🌀 Circular Motion Calculator
Calculate circular motion parameters
Leave blank if entering velocity
Leave blank if entering period
How to Use This Calculator
Enter Radius
Input the radius (r) in meters (m). This is the distance from the center of the circular path to the object. The radius must be positive and greater than zero. This is always required.
Enter Period OR Velocity
You have two options: Enter the period (T) in seconds - the time for one complete revolution, OR enter the velocity (v) in m/s - the linear speed along the circular path. Leave one blank - you only need to provide either period or velocity, not both.
Calculate and Review
Click the "Calculate" button to compute all circular motion parameters. The calculator will display: velocity (m/s), angular velocity (rad/s), period (s), and frequency (Hz). All these values are interrelated and describe the circular motion completely.
Formula
v = 2Ï€r / T
ω = 2π / T = v / r
f = 1 / T
Where:
• v = Linear velocity (m/s)
• ω = Angular velocity (rad/s)
• T = Period (s)
• f = Frequency (Hz)
• r = Radius (m)
Example 1: Using Period
An object moves in a circle of radius 5 m with a period of 10 seconds. Calculate all motion parameters.
Given:
• Radius (r) = 5 m
• Period (T) = 10 s
Solution:
v = 2πr / T = 2π × 5 / 10 = π = 3.14 m/s
ω = 2π / T = 2π / 10 = 0.628 rad/s
f = 1 / T = 1 / 10 = 0.1 Hz
Velocity: 3.14 m/s, Angular Velocity: 0.628 rad/s, Frequency: 0.1 Hz
Example 2: Using Velocity
A car moves at 20 m/s around a circular track of radius 50 m. Calculate the period and frequency.
Given:
• Radius (r) = 50 m
• Velocity (v) = 20 m/s
Solution:
T = 2πr / v = 2π × 50 / 20 = 5π = 15.71 s
ω = v / r = 20 / 50 = 0.4 rad/s
f = 1 / T = 1 / 15.71 = 0.0637 Hz
Period: 15.71 s, Angular Velocity: 0.4 rad/s, Frequency: 0.0637 Hz
Frequently Asked Questions
What is uniform circular motion?
Uniform circular motion is motion at constant speed in a circular path. The object maintains the same speed (magnitude of velocity) but the direction of velocity constantly changes, requiring a centripetal acceleration toward the center. Despite constant speed, the object is accelerating because velocity is a vector quantity.
What's the difference between linear velocity and angular velocity?
Linear velocity (v) measures how fast an object moves along its path in m/s. Angular velocity (ω) measures how fast the object rotates around the center in rad/s. They're related by v = rω, where r is the radius. For the same angular velocity, objects further from the center have higher linear velocity.
What is the relationship between period and frequency?
Period (T) is the time for one complete revolution, while frequency (f) is the number of revolutions per second. They are reciprocals: f = 1/T and T = 1/f. Higher frequency means shorter period (faster rotation). For example, if frequency is 2 Hz, period is 0.5 seconds.
Can I use this calculator if I only know the radius?
No, you need at least one more piece of information: either the period (time for one revolution) or the velocity (speed along the path). With just radius, you can't determine the motion parameters. The calculator will prompt you to enter either period or velocity.
How are these parameters used together?
These parameters are all interconnected: Knowing any two allows you to calculate the others. For example, if you know radius and period, you can find velocity, angular velocity, and frequency. They provide a complete description of uniform circular motion, allowing you to calculate centripetal force, acceleration, and other related quantities.
Where is circular motion used in real-world applications?
Circular motion is everywhere: vehicles turning corners, satellites orbiting Earth, electrons orbiting atomic nuclei, washing machine spin cycles, amusement park rides, rotating machinery, planetary motion, and many mechanical systems. Understanding these parameters is essential for designing and analyzing any rotating system.
About Circular Motion Calculator
The circular motion calculator computes velocity, angular velocity, period, and frequency for objects in uniform circular motion. These parameters are all interconnected and provide a complete description of circular motion.
This calculator is essential for students studying rotational kinematics, engineers designing rotating systems, and anyone analyzing circular or orbital motion. It allows you to calculate all motion parameters from just radius and either period or velocity, making it easy to understand and analyze circular motion in various contexts.