Circular velocity is a fundamental concept in physics and astronomy that describes The speed at which an item travels around a central point in a circular path

The term "circular velocity" is commonly used in various fields, including celestial mechanics, where it plays a imporatnt role in understanding the dynamics of the objects orbiting around the larger bodies like the planets orbiting stars or moons orbiting planets.

The rate at which an object completes a full revolution around a central point is known as its circular velocity. Both the circular path's radius and the object's orbital period have an impact on it. Larger orbits require higher velocities to sustain circular motion in the same period of time, as the formula shows that circular velocity is directly proportional to the radius of the circular path.

Formula of Circular Velocity :

The formula for circular velocity is:

Circular Velocity = 2π × Radius / Time

Where:
  • Circular Velocity is the speed at which an object moves in a circular path around a central point is known as its circular velocity.
  • π is a mathematical constant that approximately equals to 3.14159.
  • The radius measures how far an object is from the circle's center to its position.
  • Time is the duration it takes for the object to complete one full revolution around the central point.

According to this formula, the circular velocity is calculated  multiplying the circumference of the circular path (2π times the radius) by the reciprocal of the time taken to complete one full revolution. Essentially, it determines the speed at which an object travels along its circular path by calculating the rate of angular displacement of the object around a circle's center.

Units of Circular Velocity :

The units of circular velocity depend on the units used for radius and time in the formula. The formula for circular velocity is:
Circular Velocity = 2π × Radius / Time

Here are the units for each variable:

Circular Velocity : The unit of circular velocity could be expressed as distance per unit time. Common units include meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph), depending on the system of measurement being used.

π : Pi is a dimensionless mathematical constant.

Radius : The radius is a measure of length and is typically expressed in units such as meters (m), kilometers (km), feet (ft), or miles (mi), depending on the scale of the circular path.

Time : The unit of time could be seconds (s), minutes (min), hours (h), or any other time unit.

So, the units of circular velocity depend on the combination of units used for the radius and time components in the formula. For example, if the radius is in meters and time is in seconds, the units of circular velocity would be meters per second (m/s). Similarly, if the radius is in kilometers and time is in hours, the units of circular velocity would be kilometers per hour (km/h).

So here are some common units of Circular Velocity are :

  • meters per second (m/s)
  • kilometers per hour (km/h)
  • centmeters per second (cm/s)
  • miles per hour (mi/h)
  • feet per second (ft/s)
  • yards per second(yd/s)

How Circular Velocity Calculator Works: A Step-by-Step Example

Question :

A satellite is in a circular orbit around the Earth at an altitude of 500 kilometers above the Earth's surface. If it takes the satellite approximately 90 minutes to complete one orbit, what is its circular velocity?

Answer :

To find the circular velocity of the satellite, we first need to calculate the total radius of its orbit, including the altitude above the Earth's surface.
Given that the altitude of the satellite above the Earth's surface is 500 kilometers, we add this altitude to the radius of the Earth, which is approximately 6,371 kilometers.

Total radius = Altitude above Earth's surface + Radius of Earth
Total radius = 500 km + 6,371 km
Total radius = 6,871 kilometers
Next, we convert the time taken for one orbit to hours, since 90 minutes is 1.5 hours.
Now, we use the formula for circular velocity:

Circular Velocity = 2π × Radius / Time
Circular Velocity = 2 π × 6,371 km / 1.5 hours
Circular Velocity = 2 × 3.14159 × 6,371 km / 1.5 hours
Circular Velocity = 43,172.798 km / 1.5 hours
Circular Velocity = 28,781.865 km/h

Therefore, the circular velocity of the satellite in its orbit around the Earth is approximately 28,781.865 kilometers per hour.

Why to use our Circular Velocity Calculator?

Our circular velocity calculator simplifies complex calculations by instantly computing the speed at which an object orbits a central point in a circular path. It eliminates manual errors, saves time, and provides accurate results, making it a valuable tool for students, engineers, and researchers alike.